## Schedule of the meeting

### General program

**Sunday June 24**

**Monday June 25**

Rector of the Charles University

Dean of the Faculty of Mathematics and Physics

**Marek Abramowicz**

Innermost part of accretion disks around black holes

**Abstract: **Einstein's general relativity makes fundamental predictions about the latest, strong-field, stages of accretion, when matter plunges from the accretion disk into the black hole. They include * location of the plunge-in region, * efficiency of the black hole accretion, * nature of torques in the plunge-in region, * extracting energy from the black hole. The 1977 Blandford \& Znajek prediction that energy may be extracted from a rotating black hole by an electromagnetic version of the Penrose process was convincingly proven in recent super-computer simulations of the "arrested" accretion of magnetized matter by Tchekhovskoy, McKinney and Narayan${}^*$. Another version of the Penrose process, involving energetic particle collisions near the horizon, has been discussed by Piran and collaborators already in the 1970. These classic works (and their recent follow-up, also by Piran and collaborators) proved that this process can neither extract a significant amount of energy from the black hole nor accelerate particles to large energies. ${}^*$ Ramesh Narayan's lecture describes these simulations.

Back to program

Monday | Tuesday | Wednesday | Thursday | Friday | |
---|---|---|---|---|---|

8:30 | J. Bičák | G. Gibbons | B. Schutz | T. Damour | 8:50 A. Hamilton |

9:10 | J. Barbour | M. Sasaki | D. Sudarsky | G. Schäfer | G. Neugebauer |

9:50 | Coffee break | ||||

10:30 | C. Will | A. Ashtekar | H. Friedrich | L. Rezzolla | L. Andersson |

11:10 | P. Schneider | A. Starobinsky | H. Nicolai | J. Lewandowski | R. Wald |

11:50 | Lunch | ||||

13:50 | M. Kramer | C. Clarkson | J. Friedman | L. Barack | M. Mars |

14:30 | R. Narayan | H. Reall | G. Gonzalez | A. Rostworowski | D. Bini |

15:00 | M. Abramowicz | V. Frolov | G. Heinzel | Poster session with refreshments | Coffee break |

15:30 | Coffee break | Parallel sessions | |||

16:00 | Parallel sessions | Parallel sessions |

16:15 Honorary degreeceremony |
16:15 Tour |
17:50 Conference closing |
|||

17:30 Reception |
18:45 Organ concert inSt.Vitus Catedral |
||||

19:30 Concert |
20:00 Public lecture |
19:30 Banquet |

### Parallel sessions - Monday

Blue lecture hall | Red lecture hall | Yellow lecture hall | |||
---|---|---|---|---|---|

16:00 | S. Dain | D. Lynden-Bell | J. Pullin | ||

16:15 | J. Valiente Kroon | H. Pfister | M. Dupuis | ||

16:30 | O. Rinne | C. Schmid | S. Major | ||

16:45 | H. Andreasson | D. Giulini | Y. Bonder | ||

17:00 | Break | ||||

17:15 | J. Senovilla | N. Dadhich | D. Konkowski | ||

17:30 | T. Bäckdahl | L. Sokolowski | V. Balek | ||

17:45 | C. Cederbaum | L. Lusanna | J. Mielczarek | ||

18:00 | F. Schuller | J. Garecki | A. Gorlich | ||

18:15 | N. Gürlebeck | S. Sarkar | I. Khavkine |

### Parallel sessions - Wednesday

Blue lecture hall | Red lecture hall | Yellow lecture hall | |||
---|---|---|---|---|---|

16:00 | A. Hamilton | R. Sussman | A. Corichi | ||

16:15 | M. Lyutikov | D. Wiltshire | S. Gielen | ||

16:30 | D. Psaltis | N. Pinto-Neto | T. Roman | ||

16:45 | G. Loukes-Gerakopoulos | S. Carneiro | F. Girelli | ||

17:00 | Break | ||||

17:15 | E. Hackmann | J. Larena | M. Krämer | ||

17:30 | S. Gralla | G. Marozzi | F. Hinterleitner | ||

17:45 | G. Dotti | P. Helbig | L. Hodgkinson |

### Parallel sessions - Friday

Blue lecture hall | Red lecture hall | Yellow lecture hall | |||
---|---|---|---|---|---|

15:30 | T. Koslowski | B. Iyer | A. Le Tiec | ||

15:45 | H. Maeda | J. Nester | E. Barausse | ||

16:00 | D. Kubiznak | L. Szabados | M. Zilhão | ||

16:15 | A. Pravdová | M. Jasiulek | O. Kopáček | ||

16:30 | Break | ||||

16:45 | A. Anabalon | I. Rácz | M. Crosta | ||

17:00 | A. Zelnikov | G. Fodor | J. Svoboda | ||

17:15 | J. Podolský | C. Chirenti | J. Horák | ||

17:30 | M. Cariglia | M. Salgado | D. Malafarina |

## Monday June 25

### Registration

Rector of the Charles University

Dean of the Faculty of Mathematics and Physics

### Plenary Session in Blue Lecture Hall

- location of the plunge-in region,
- efficiency of the black hole accretion,
- nature of torques in the plunge-in region,
- extracting energy from the black hole.

**Jiří Bičák**

Einstein's Days and Works in Prague: Relativity Then and Now

**Jiří Bičák**

Einstein's Days and Works in Prague: Relativity Then and Now

**Abstract: **It was during his stay in Prague when Einstein started in earnest to
develop his ideas about general relativity. I will evoke those
days in 1911 and 1912, discuss Einstein's papers on gravitation from
that period, emphasize which new concepts and ideas he introduced.
I also want to indicate how the main themes that preoccupied him then,
the principle of equivalence, bending of light, gravitational redshift
and frame dragging effects are alive in contemporary relativity.

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**Julian Barbour**

Prague and the conception of general relativity: Kepler, Mach and Einstein

**Julian Barbour**

Prague and the conception of general relativity: Kepler, Mach and Einstein

**Abstract: **In the first part of my talk, I shall argue that Kepler's discovery of his first two laws of planetary motion in Prague in the years 1600 to 1605 can be seen as the first success of Mach's principle. Kepler's intuition was quite unlike that of his predecessors and Newton and strikingly similar to Mach's. In view of the considerable confusion surrounding Mach's principle, I shall try to identify his key ideas, which included a relational treatment of not only position but also time. I will also discuss a penetrating analysis by Poincare of a predictive defect that is revealed when one expresses Newtonian dynamics in relative quantities. On this basis one can formulate a precise criterion that a Machian theory of motion should satisfy. I shall then consider why Einstein did not make any serious attempt to implement a theory of relativity directly along the lines suggested by Mach's and Poincare's ideas and instead followed a brilliantly successful indirect strategy. Finally, I shall consider whether purely historical accidents - such as the creation of general relativity before quantum mechanics - could be closing our minds to new conceptions of time and motion.

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**Clifford Will**

Testing general relativity: Centenary highlights and future prospects

**Clifford Will**

Testing general relativity: Centenary highlights and future prospects

**Abstract: **During the latter part of the 20th century, general relativity was well-tested in the weak-field slow-motion regime of the solar system. In binary pulsar systems, some tests of strong-field aspects of the theory were carried out. We will give a brief overview of these achievements. As we look to the post-centenary future, testing GR in the strong-field, highly dynamical regime will be an important theme in experimental relativity. We will describe a number of possible tests that could be carried out, including tests using astrophysical phenomena around black holes, tests using gravitational waves, and tests of black hole no-hair theorems using high-precision observations of stars orbiting our galactic center black hole.

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**Peter Schneider**

Gravitational light bending: a powerful astrophysical tool

**Peter Schneider**

Gravitational light bending: a powerful astrophysical tool

**Abstract: **Originally being the first crucial test of General Relativity, light
deflection in a gravitational field has become one of the prime tool
for astrophysics and cosmology, with applications ranging from the
detection of extra-Solar planets, the study of the (dark) matter
distribution in galaxies and galaxy clusters, the use as natural
telescopes which come for free, the biasing properties of galaxies, to
constraining the equation-of-state of dark energy and testing the law
of gravity on cosmic scales. In this talk, a selection of recent
research highlight will be presented, and prospects for future
developments will be given.

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**Michael Kramer**

Einstein's gravity as seen by a cosmic lighthouse keeper

**Michael Kramer**

Einstein's gravity as seen by a cosmic lighthouse keeper

**Abstract: **We can only speculate but presumably Albert Einstein would be delighted to see the experiments possible today that are made to test his theory of gravity. Among the most precise ones are tests with binary pulsars, which provide in particular information about the strong-field regime. From observations of pulsars we can test a large variety of relativistic effects or concepts deeply embedded in the framework of theories of gravity, including the existence of gravitational waves or the validity of the strong equivalence principle. This talk summarizes the latest experiments and tests provided by the cosmic lighthouses that we call pulsars. The corresponding observations provide the best limits on the validity of general relativity and alternative theories of gravity.

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**Ramesh Narayan**

Energy Extraction from Spinning Black Holes: Relativistic Jets

**Ramesh Narayan**

Energy Extraction from Spinning Black Holes: Relativistic Jets

**Abstract: **A deep idea in black hole physics is that it is possible to extract
energy from a spinning black hole. It has for long been an article of
faith among astrophysicists that black hole spin power is somehow
responsible, perhaps via magnetic fields, for the relativistic jets
seen in accreting black holes. Two recent advances have strengthened
the case for this thesis.

First, spin parameters of a number of accreting stellar-mass black
holes have been measured. It is found that relativistic jets from more
rapidly spinning black holes have substantially larger radio power
than those from slowly spinning black holes. This observational
evidence strongly suggests a causal relationship between black hole
spin and jets.

Second, numerical magnetohydrodynamic simulations of accreting black
holes show that relativistic jets appear spontaneously in such
systems. For a while it was unclear whether the power source for the
jets is the accretion disk or the spin of the black hole. Recent work
has produced unambiguous evidence that much of the energy flows out of
the black hole and into the jet via magnetic fields.

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**Marek Abramowicz**

Innermost part of accretion disks around black holes

**Marek Abramowicz**

Innermost part of accretion disks around black holes

**Abstract: **Einstein's general relativity makes
fundamental predictions about the latest,
strong-field, stages of accretion, when
matter plunges from the accretion disk
into the black hole. They include

Another version of the Penrose process, involving energetic particle collisions near the horizon, has been discussed by Piran and collaborators already in the 1970. These classic works (and their recent follow-up, also by Piran and collaborators) proved that this process can neither extract a significant amount of energy from the black hole nor accelerate particles to large energies.

${}^*$ Ramesh Narayan's lecture describes these simulations.

Back to program

### Parallel Session in Blue Lecture Hall

**Sergio Dain**

Geometric inequalities for black holes

**Sergio Dain**

Geometric inequalities for black holes

**Abstract: **A geometric inequality in General Relativity relates quantities
that have both a physical interpretation and a geometrical
definition. It is well known that the parameters that
characterize the Kerr-Newman black hole satisfy several
important geometric inequalities. Remarkably enough, some of
these inequalities also hold for dynamical black holes. This
kind of inequalities, which are valid in the dynamical and
strong field regime, play an important role in the
characterization of the gravitational collapse. They are closed
related with the cosmic censorship conjecture. In this talk I
will review recent results in this subject.

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**Juan Valiente Kroon**

A class of conformal curves for spherically symmetric spacetimes

**Juan Valiente Kroon**

A class of conformal curves for spherically symmetric spacetimes

**Abstract: ** I will discuss a class of conformally privileged curves on spherically symmetric spacetimes. The class of curves under consideration provides a natural generalization of the notion of conformal geodesics for non-vacuum spacetimes. Like conformal geodesics in vacuum spacetimes, these curves can be arranged so that they provide a canonical conformal factor which can be read from the data of the curve. Of particular interest for our analysis are spacetimes containing black hole regions. A natural question in this context is whether the congruence of curves can cover the whole of the outer domain of communication of these spacetimes without forming conjugate points. When this is the case, the congruence can be used to construct “generalized Gaussian coordinates” by means of which one can evaluate (numerically) a conformal representation of the spherically symmetric spacetime. Special attention will be given, in this analysis, to the Reissner-Nordström (non-extremal and extremal), Schwarschild-de Sitter, Schwarzschild-anti de Sitter and Vaydia spacetimes.

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**Oliver Rinne**

Evolution of the Einstein equations to future null infinity

**Oliver Rinne**

Evolution of the Einstein equations to future null infinity

**Abstract: **Given that gravitational radiation is only defined unambiguously at future null infinity $\cal J^+$, it is very desirable to include $\cal J^+$ in numerical evolutions of the Einstein equations. We choose to work directly with the Einstein equations (in an ADM-like reduction with elliptic gauge conditions) expressed in terms of a conformal metric. The resulting equations develop apparently singular terms at $\cal J^+$ that can nevertheless be evaluated in a regular way through an enforcement of the constraint equations. Stable numerical evolutions of a perturbed Schwarzschild black hole in axisymmetry have been obtained. We also show how matter can be included in our formalism and present numerical Einstein-matter evolutions in spherical symmetry.

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**Hakan Andreasson**

Black hole formation from a complete regular past for collisionless matter

**Hakan Andreasson**

Black hole formation from a complete regular past for collisionless matter

**Abstract: **Initial data for the spherically symmetric Einstein-Vlasov system is constructed whose past evolution is regular and whose future contains a black hole. This is the first example of initial data with these properties for the Einstein-matter system with a "realistic" matter model. One consequence of the result is that there exists a class of initial data for which the ratio of the Hawking mass and the area radius is arbitrarily small everywhere, such that a black hole forms in the evolution. Another consequence is that there exist black hole initial data such that the solutions exist for all Schwarzschild time.

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**José M Senovilla**

On the stability operator for MOTS and the `core' of Black Holes

**José M Senovilla**

On the stability operator for MOTS and the `core' of Black Holes

**Abstract: **I will consider small deformations of marginally (outer) trapped surfaces (MOTS) by using the stability operator introduced by Andersson-Mars-Simon. In the case of spherical symmetry, one can use these deformations on any marginally trapped round sphere placed at the spherically symmetric marginally trapped tube (MTT) -defined by $r=2m$- to prove several interesting results as well as the following surprising and fundamental theorem: "In spherically symmetric spacetimes, there are closed trapped surfaces (topological spheres) penetrating both sides of the spherical (non-null) MTT with arbitrarily small portions inside the region $r<2m$".

Then, the concept of `core' of a black hole is introduced: it is the minimal region that one should remove from the spacetime in order to get rid of all possible closed trapped surfaces. In spherical symmetry, and using the previous theorem, one can prove that the spherical MTT is the boundary of a core.

By using a novel formula for the principal eigenvalue of the stability operator, I will argue that similar results may hold in general black hole spacetimes.

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**Thomas Bäckdahl**

How to measure deviation from the Kerr initial data -- recent progress

**Thomas Bäckdahl**

How to measure deviation from the Kerr initial data -- recent progress

**Abstract: **In this talk I will present recent progress concerning a construction of a geometric invariant for initial data sets for the Einstein vacuum field equations. This geometric invariant vanishes if and only if the initial data set corresponds to data for the Kerr spacetime, and thus, it characterizes this type of data. This construction is based on Killing spinors and have now been carried out for compact domains and domains reaching the asymptotically flat ends. We investigate properties of this invariant.

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**Carla Cederbaum**

The Geometry of Static Spacetimes: Geometrostatics

**Carla Cederbaum**

The Geometry of Static Spacetimes: Geometrostatics

**Abstract: **Geometrostatics is an important subdomain of Einstein's General Relativity. It describes the mathematical and physical properties of static isolated relativistic systems such as stars, galaxies or black holes. For example, geometrostatic systems have a well-defined ADM-mass (Chrusciel, Bartnik) and (if this is nonzero) also a center of mass (Huisken-Yau, Metzger) induced by a CMC-foliation at infinity. We will present localized surface integral formulas for these physical properties in general geometrostatic systems. Together with an asymptotic analysis, these can be used to prove that ADM-mass and center of mass 'converge' to the Newtonian mass and center of mass in the Newtonian limit $c\to\infty$ (using Ehler's frame theory). We will discuss geometric similarities of geometrostatic and classical static Newtonian systems along the way.

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**Frederic Schuller**

Geometrodynamics beyond Einstein

**Frederic Schuller**

Geometrodynamics beyond Einstein

**Abstract: **Which alternative geometries on a smooth manifold can serve as a spacetime structure? And what are their gravitational dynamics? In this talk I will show that these questions
surprisingly have rather comprehensive answers, if one employs an intriguing interplay of real algebraic geometry, convex analysis and the theory of hyperbolic polynomials.

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**Norman Gürlebeck**

Source integrals for Geroch's Multipole Moments

**Norman Gürlebeck**

Source integrals for Geroch's Multipole Moments

**Abstract: **Geroch's multipole moments of a stationary spacetime are defined by the asymptotic behavior of its metric near spatial infinity. They can be used to describe the spacetime sufficiently far away from the source. However, their relation to the source itself is only clarified for the leading multipole moments -- the mass and, in case of axially symmetry, the angular momentum -- via the Komar integrals. We describe here an algorithm to derive such source integrals for stationary and axially symmetric spacetimes also for higher multipole moments and give the first few examples explicitly. In the special case of staticity, we give all multipole moments in such a local form.

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### Parallel Session in Red Lecture Hall

**Donald Lynden-Bell**

Strong Gravomagnetism and Gravitational Solenoids

**Donald Lynden-Bell**

Strong Gravomagnetism and Gravitational Solenoids

**Abstract: **In electromagnetism a current along a wire tightly wound on a torus makes a solenoid whose magnetic field is confined within the torus. In Einstein's gravity we give a corresponding solution in which a current of matter moves up on the inside of a toroidal shell and down on the outside, rolling around the torus by the short way. The metric is static outside the torus but stationary inside with the gravomagnetic field confined inside the torus, running around it by the long way. This exact solution of Einstein's equations is found by fitting Bonnor's solution for the metric of a light beam, which gives the required toroidal gravomagnetic field inside the torus, to the general Weyl static external metric in toroidal coordinates, which we develop. We deduce the matter tensor on the torus and find when it obeys the energy conditions. We also give the equipotential shells that generate the simple Bach–Weyl metric externally and find which shells obey the energy conditions.

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**Herbert Pfister**

Gravitomagnetism: From Einstein's 1912 paper to the satellites LAGEOS and Gravity Probe B

**Herbert Pfister**

Gravitomagnetism: From Einstein's 1912 paper to the satellites LAGEOS and Gravity Probe B

**Abstract: **In a short 1912 paper Einstein asked whether there exists a gravitational action analogous to electrodynamic induction. He introduced the model of an infinitely thin spherical mass shell, and derived that a test mass at its center is dragged along if the mass shell is linearly accelerated. Later Einstein and Besso (in the Entwurf theory) and Lense and Thirring (in GR) derived a rotational dragging of test masses inside a mass shell and outside a rotating full body (e.g. the earth), but only in the weak field and small rotation limit. Brill, Cohen (1966) and Pfister, Braun (1985) generalized this to strong fields and to higher order rotation, in this way confirming Machian ideas in GR, and proposing a "quasiglobal principle of equivalence". Recently this new "gravitomagnetic force" was experimentally confirmed by the satellites LAGEOS and Gravity Probe B.

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**Christoph Schmid**

Exact dragging of inertial axes by cosmic energy currents on the past light-cone

**Christoph Schmid**

Exact dragging of inertial axes by cosmic energy currents on the past light-cone

**Abstract: **We prove exact rotational dragging of spin axes of gyroscopes (= inertial axes) by cosmic
energy-currents on the past light-cone of a gyroscope for linear perturbations with
arbitrary energy-flows of arbitrary matter.

Our proof demonstrates that the principle
postulated by Mach holds for linear cosmological perturbations. Gyroscopes are "in the
absolute grip of the distant universe" with the weight function peaked for matter
(galaxies etc) at redshift $z = 1$.

For sub-Hubble distances between gyroscope and
energy-currents, the mechanism for dragging of the gyroscope's spin axis is the same
as in Ampere's law of magnetism except for a sign change. For distances larger than
the Hubble radius, $z \approx 1$, and back to the big bang, there is an exponential
suppression of the influence of energy currents on our gyroscopes.

For arbitrary
fields of energy currents, we show that the precession of the spin axis of a gyroscope
can be caused only by the vector-spherical-harmonic components of the energy currents
in the toroidal vorticity sector and with angular momentum $\ell = 1$ relative to the
gyroscope. For every infinitesimal distance interval, this harmonic component is equal
to the gravito-magnetic moment and also equal to half of the kinetic angular momentum of
the arbitrary energy-current distribution. The corresponding Einstein equation is the
Ricci $R^{v \phi} = C T^{v \phi}$ equation, where $v$ is the retarded time, which is
constant on the past light-cone of the gyroscope. This Einstein equation is the angular
momentum constraint on the past light-cone.

A crucial element is our proof that the
intrinsic geometry of any light-cone cannot be perturbed by toroidal vorticity currents.
We choose coordinates on the past light-cone of the gyroscope such that the metric
coefficients $g_{\mu \nu}$ are unperturbed.

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**Domenico Giulini**

Another perspective on Einstein's "Prague" field equation of 1912

**Domenico Giulini**

Another perspective on Einstein's "Prague" field equation of 1912

**Abstract: **During his time in Prague, Einstein searched for modifications of Newtonian gravitational field equation for static fields and arrived at a non-linear equation for a scalar field that, as it turns out retrospectively, shares some qualitative features with General Relativity (GR). In my talk I will show how to arrive at this equation form a procedure that merely requires a self consistent implementation of the gravitational field's self-energy in Newtonian gravity. This procedure is the analog of the derivation of GR starting from a Poincare
invariant zero-mass spin-2 theory in Minkowski space (known as the "flat" approach to GR) and the requirement of consistent self coupling.

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**Naresh Dadhich**

Universal Features of the Lovelock Gravity

**Naresh Dadhich**

Universal Features of the Lovelock Gravity

**Abstract: **We will explore the universal properties of the Lovelock gravity. It turns out that for the static pure Lovelock black holes, the thermodynamical parameters always bear the same relation to the horizon radius indicating the thermodynamical universality. Further the pure Lovelock vacuum in the odd critical $d=2n+1$ dimension is defined by the vanishing of the higher order Riemann analogue tensor. However the spacetime is not Riemann flat and it is characterized by the solid angle deficit which gives rise to the Einstein stresses conforming to that of a global monopole asymptotically. By adding $\Lambda$, we obtain the BTZ black hole in $d=2n+1$ dimension.

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**Leszek Sokolowski**

The twin paradox in static spacetimes and Jacobi fields

**Leszek Sokolowski**

The twin paradox in static spacetimes and Jacobi fields

**Abstract: **The twin paradox in special relativity has a clear geometrical meaning, yet in
most textbooks its resolution is given only in the simplest case and provides
no deeper understanding of the effect. Vaguely speaking, in flat spacetime
the twin moving at a higher nonuniform velocity is the younger one. In
curved spacetimes a multitude of possibilities occur and the simplest case
in Schwarzschild spacetime, a non-geodesic twin at (absolute) rest and a
geodesic twin moving on a circular orbit, is in some sense misleading. In
general one can only determine which worldline connecting the separation
and the reunion point makes the twin following it the oldest one. This is the
timelike geodesic without points conjugate to the initial (separation) point
on the segment ending at the reunion point. The conjugate points exist if any
Jacobi vector field (any solution of the geodesic deviation equation) vanishes
at a point provided that the field vanishes at the initial point. We therefore
investigate Jacobi fields on timelike geodesics in a number of static space-
times. For physical reasons we study only simplest geodesic curves: circular
orbits (if they exist) and radial trajectories (flights upwards and downwards)
and calculate their lengths. For comparison we compute the length of a
non-geodesic worldline of a static observer between the separation and the
reunion. In all the spacetimes under consideration the radial geodesics are
the longest ones and except de Sitter space they contain conjugate points
outside the relevant segment; there may be two points or an infinite sequence
of conjugate points. All static spherically symmetric spacetimes have
the same properties concerning circular geodesics (if they exist): there exist
two infinite sequences of conjugate points. We also compare the radial time-
like geodesics in Robertson-Walker spacetime with these in static metrics
and find qualitative similarities. The Jacobi fields may be effectively studied
only in spacetimes with a high symmetry since the existence of integrals of
motion generated by Killing vector fields is crucial for solving the geodesic
deviation equation.

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**Luca Lusanna**

Canonical gravity, non-inertial frames, relativistic metrology and dark matter

**Luca Lusanna**

Canonical gravity, non-inertial frames, relativistic metrology and dark matter

**Abstract: **Clock synchronization leads to the definition of
instantaneous 3-spaces (to be used as Cauchy surfaces) in
non-inertial frames, the only ones allowed by the equivalence
principle. ADM canonical tetrad gravity in asymptotically
Minkowskian space-times can be described in this framework. This
allows to find the York canonical basis in which the inertial
(gauge) and tidal (physical) degrees of freedom of the gravitational
field can be identified. A Post-Minkowskian linearization with
respect to the asymptotic Minkowski metric (asymptotic background)
allows to solve the Dirac constraints in non-harmonic 3-orthogonal
gauges and to find non-harmonic TT gravitational waves. The inertial
gauge variable York time (the trace of the extrinsic curvature of
the 3-space) describes the general relativistic freedom in clock
synchronization. After a digression on the gauge problem in general
relativity and its connection with relativistic metrology, it is shown that dark matter, whose experimental signatures are the rotation curves and the mass of galaxies, may be described (at least partially) as an inertial relativistic effect (absent in Newton gravity) connected with the York time, namely with the non-Euclidean nature of 3-spaces as 3-sub-manifolds of space-time.

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**Janusz Garecki**

Canonical superenergy tensors: a reappraisal

**Janusz Garecki**

Canonical superenergy tensors: a reappraisal

**Abstract: **In the framework of general relativity (GR) the gravitational field has no energy-momentum tensor. But it is very easy to attach to this field a ``superenergy tensor''. In the Lecture we present an universal and constructive definition of such a tensor. This definition uses locally Minkowskian structure of the spacetime in GR and canonical energy-momentum complex for matter and gravity in this theory.
The obtained canonical superenergy tensor for gravity is very closely related to Appel's ``energy of acceleration'' in classical mechanics.
Applied to matter tensor our procedure leads to superenergy tensor for matter.
We have used in past the superenergy tensors, gravitation and matter, to analysis of the majority solutions to the Einstein equations which are interesting in astrophysics and cosmology. The obtained results were interesting (they were published).
By slightly changing our constructive definition of the superenrgy tensors one can obtain the averaged relative energy-momentum tensors. These tensors have proper dimensions and they differ from the superenergy tensors only by a dimensional factor which needs fixing.
We have given a proposal how to establish this factor.

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**Sudipta Sarkar**

Entropy increase during physical processes for black holes in Lanczos-Lovelock gravity

**Sudipta Sarkar**

Entropy increase during physical processes for black holes in Lanczos-Lovelock gravity

**Abstract: **We study quasi-stationary physical process for black holes within the context of Lanczos-Lovelock gravity. We show that the Wald entropy of stationary black holes in Lanczos-Lovelock gravity monotonically increases for quasi-stationary physical processes in which the horizon is perturbed by the accretion of positive energy matter and the black hole ultimately settles down to a stationary state. This result reinforces the physical interpretation of Wald entropy for Lanczos-Lovelock models and takes a step towards proving the analogue of the black hole area increase-theorem in a wider class of gravitational theories.

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### Parallel Session in Yellow Lecture Hall

**Jorge Pullin**

A local Hamiltonian for spherically symmetric gravity coupled to a scalar field

**Jorge Pullin**

A local Hamiltonian for spherically symmetric gravity coupled to a scalar field

**Abstract: **We present a gauge fixing for gravity coupled to a scalar field in spherical symmetry that leads to a true Hamiltonian that is the integral over space of a local density. We discuss its potential use to study black hole evaporation.

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**Maite Dupuis**

Loop Quantum gravity in terms of spinors and harmonic oscillators

**Maite Dupuis**

Loop Quantum gravity in terms of spinors and harmonic oscillators

**Abstract: **Loop Quantum Gravity is an attempt to quantize general relativity. Its kinematical aspects are well understood and yield a description of space in terms of quanta.
Spinorial tools provide a really nice geometrical picture of the classical phase space of Loop Gravity. Moving to the quantum level, spinors are simply quantized as harmonic oscillators. They are then the building blocks to define coherent states for Loop Quantum Gravity and to build spinfoam models which is a regularized path integral for general relativity.
I will recall the main results of the spinorial formalism in the context of Loop Quantum Gravity and Spinfoam models and explain how it can be generalized to introduce a cosmological constant into the game.

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**Seth Major**

On the Observability of Granularity of Spatial Geometry

**Seth Major**

On the Observability of Granularity of Spatial Geometry

**Abstract: **If quantum geometry is an accurate model of microscopic spatial geometry then two related questions arise, one observational and one theoretical: How and at what scale is the discreteness manifest? How is the general relativistic limit achieved? These questions will be discussed in the context of studies of a single atom of geometry. It will be shown that the effective scale of the discreteness could be much larger than the Planck scale. Before this scale can be predicted, the relations between discrete geometry, coherent states, and the semiclassical limit need to be clarified. Work towards this goal, using coherent states in spin foams, the spin geometry theorem of Penrose and Moussouris, and twisted geometries will be described.

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**Yuri Bonder**

Quantum Gravity Phenomenology without Lorentz Invariance Violations

**Yuri Bonder**

Quantum Gravity Phenomenology without Lorentz Invariance Violations

**Abstract: **In the last years the phenomenology of quantum gravity has been dominated by the search of violations of Lorentz symmetry. However, there are very serious arguments that led us to assume that Lorentz invariance is a real symmetry in Nature. This motivated us to construct a phenomenological model describing how a Lorentz invariant discrete structure of spacetime could become manifest. The proposal is fully observer covariant, it involves non-trivial couplings of curvature to matter fields and leads to a well defined phenomenology. In fact, an experiment specially designed to test the model has been performed by the Eöt-Wash group allowing to put bounds on some of the model's free parameters.

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**Deborah Konkowski**

Quantum singularities in static and conformally static space-times

**Deborah Konkowski**

Quantum singularities in static and conformally static space-times

**Abstract: **The definition of quantum singularity is extended from static space-times to conformally static space-times. After the usual definitions of classical and quantum singularities are reviewed, examples of quantum singularities in static space-times are given. These include asymptotically power-law space-times, space-times with diverging higher-order differential invariants, and a space-time with a 2-sphere singularity. The theory behind quantum singularities in conformally static space-times is followed by several examples: a Friedmann-Robertson-Walker space-time with cosmic string, Roberts space-time, Fornav space-time, and the HMN metric. Future areas of research are discussed.

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**Vladimír Balek**

From 'nothing' to inflation and back again

**Vladimír Balek**

From 'nothing' to inflation and back again

**Abstract: **Solutions of Wheeler-DeWitt equation in a minisuperspace with massive scalar field are constructed, following step by step the procedure developed for the description of a particle escaping from a two-dimensional potential well by Banks, Bender and Wu. For an inflationary universe driven by an unstable and metastable false vacuum, the solution describing tunneling of a universe from 'nothing' and the no-boundary solution are obtained, respectively. New features of the solutions coming from the indefinite metric in the kinetic term are pointed out and possible implications of the solutions for the theory of vacuum decay via Hawking-Moss and Coleman-de Lucia instantons are discussed.

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**Jakub Mielczarek**

Signature change in loop quantum cosmology

**Jakub Mielczarek**

Signature change in loop quantum cosmology

**Abstract: **The Wick rotation is commonly considered only as an useful
computational trick. However, as it was suggested by Hartle
and Hawking already in early eighties, Wick rotation may
gain physical meaning at the Planck epoch. While such possibility
is conceptually interesting, leading to no-boundary proposal,
mechanism behind the signature change remains mysterious.

In this talk we show that the signature change anticipated by
Hartle and Hawking may occur in result of the loop quantum
gravity effects. Theory of cosmological perturbations with the
effects of quantum holonomies is constructed. It is shown that
such theory can be uniquely formulated in the anomaly-free
manner. The algebra of quantum constraints turns out to be
modified such that the signature is changing from Lorentzian
in low curvature regime to Euclidean in high curvature regime.
Implications of this phenomenon on propagation of cosmological
perturbations are discussed. Possible relations with other
approaches to quantum gravity are also outlined.

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**Andrzej Gorlich**

A transfer matrix model of volume fluctuations in 4D Causal Dynamical Triangulations

**Andrzej Gorlich**

A transfer matrix model of volume fluctuations in 4D Causal Dynamical Triangulations

**Abstract: **Causal Dynamical Triangulation (CDT) is a background independent approach to quantum gravity. We introduce a phenomenological transfer matrix model, where at each time step we use a reduced set of quantum states characterized solely by the discretized spatial volume.
Using computer simulations we determine the transfer matrix elements in this representation and extract the effective action for the scale factor in the de Sitter phase of the 4D Causal Dynamical Triangulations. In this framework no degrees of freedom are frozen, however,
the obtained effective action agrees with the 'minisuperspace' model. We show that the observed probability distribution of spatial volume in the 'stalk' region is dominated by
the quantum state with the largest eigenvalue and that the structure of the covariance matrix can be fully explained in the language of the transfer matrix.

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**Igor Khavkine**

Time delay observable in classical and quantum geometries

**Igor Khavkine**

Time delay observable in classical and quantum geometries

**Abstract: **A class of diffeomorphism invariant, physical observables, so-called astrometric observables, is introduced. A particularly simple example, the time delay, which expresses the difference between two initially synchronized proper time clocks in relative inertial motion, is analyzed in detail. It is found to satisfy some interesting inequalities related to the causal structure of classical Lorentzian spacetimes. Thus it can serve as a probe of causal structure and in particular of violations of causality. A quantum model of this observable as well as the calculation of its variance due to vacuum fluctuations in quantum linearized gravity are sketched. The question of whether the causal inequalities are still satisfied by quantized gravity, which is pertinent to the nature of causality in quantum gravity, is raised, but it is shown that perturbative calculations cannot provide a definite answer. Some potential applications of astrometric observables in quantum gravity are discussed.
[arXiv:1111.7127]

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## Tuesday June 26

### Plenary Session in Blue Lecture Hall

**Gary Gibbons**

Links between general relativity and other parts of physics

**Gary Gibbons**

Links between general relativity and other parts of physics

**Abstract: **Now that General Relativity has become such a central part of modern physics, its geometrical formalism being taught as part of almost all undergraduate physics courses, it is natural to ask: how can its basic concepts and techniques be used to illuminate areas of physics which have no connection with gravity. Another way of asking this question is: are the analogues situations to those occurring in General Relativity. The search for such analogues
is of course an old one, but recently, because of advances in technology, these questions have become more topical. In this talk I will illustrate this theme by examples drawn from optics, acoustics, liquid crystals, graphene and the currently popular topic of cloaking.

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**Misao Sasaki**

Inflation and birth of cosmological perturbations

**Misao Sasaki**

Inflation and birth of cosmological perturbations

**Abstract: **The idea that there was a period of accelerated expansion in the very early
universe, inflation, has been extremely successful in explaining the large
scale structure of the present universe. In this talk, I review recent
developments in the theory of inflation and its predictions, particularly
those on cosmological perturbations.

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**Abhay Ashtekar**

Loop quantum gravity and the very early universe

**Abhay Ashtekar**

Loop quantum gravity and the very early universe

**Abstract: **
Since the standard cosmological perturbation theory is based on
QFT on curved space-times, it is not applicable in the Planck
era. Using techniques from loop quantum gravity, the theory is
extended to overcome this limitation. The new framework
sharpens conceptual issues by distinguishing between true and
apparent trans-Planckian difficulties and shows that the true
difficulties can be generically overcome in the standard
inflationary scenario, with interesting lessons for both theory
and observations. The talk will be based largely on some
recently completed joint work with Ivan Agullo and William
Nelson.

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**Alexei Starobinsky**

f(R) gravity - the most straightforward generalization of the Einstein gravity

**Alexei Starobinsky**

f(R) gravity - the most straightforward generalization of the Einstein gravity

**Abstract: **f(R) gravity where R is the Ricci scalar represents the simplest non-perturbative generally covariant generalization of the Einstein gravity where it is possible to avoid the appearance of new ghost and tachyon degrees of freedom. Thus, this theory can be considered at the same level of generality as general relativity, not in some perturbative regime only. It represents a particular case of scalar-tensor gravity in the limit of the zero Brans-Dicke
parameter, but with a non-zero scalar field potential. Its most interesting applications in cosmology are related to the possibility to use it for description of both types of dark energy which have appeared during the Universe evolution: primordial dark energy driving inflation in the early Universe and present dark energy which has much smaller effective energy density. In the case of inflation, the simplest $(R+R^2)$ model proposed already in 1980 is internally consistent, has a graceful exit to the radiation-dominated FRW stage via the period of reheating in which all matter in the Universe arises as a result of gravitational particle creation, and remains in agreement with the most recent observational data. Moreover, this form of f(R) may be justified by a number of microscopic models. In particular, it describes the gravitational sector of the Higgs inflation. It is possible to construct models describing the present dark energy in f(R) gravity which satisfy all present observational tests. However, these models require a much more complicated form of f(R) and a very low energy scale, so there is no microscopic justification of them at present. More critical is that these models generically cannot reproduce the correct evolution of the Universe in the past due to formation of additional weak singularities and other problems. Thus, to construct complete cosmological models of present dark energy not destroying all previous achievements of the early Universe cosmology including the recombination, the correct BBN and inflation of any kind, one has to change the behaviour of f(R) at large positive R and to extend f(R) to the region of negative R. I describe correct ways to do it. Combined description of primordial and present dark energy using one f(R) function is possible, too, but it leads to completely different reheating after inflation during which strongly non-linear oscillations of R occur.

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**Chris Clarkson**

Dark Energy and Inhomogeneity

**Chris Clarkson**

Dark Energy and Inhomogeneity

**Abstract: **Most aspects of structure formation in the late universe are treated using Newtonian gravity, either using perturbation theory or N-body simulations. General relativistic corrections to this picture are generally assumed to be 'small'. Surprisingly, not a lot is known about them however, which has led to some speculation that dark energy may in fact be relativistic aspects of structure formation in disguise. While this idea seems implausible to many, it does appear that relativistic corrections to the standard model come in at the percent level or larger. This will be important for precision cosmology and our interpretation of dark energy.

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**Harvey Reall**

Higher dimensional black holes

**Harvey Reall**

Higher dimensional black holes

**Abstract: **I shall review what is known about black holes in higher dimensions. I shall discuss the known explicit solutions, results concerning the classification of stationary black holes, and instabilities of rotating black holes in higher dimensions.

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**Valeri Frolov**

Black holes, hidden symmetry and complete integrability

**Valeri Frolov**

Black holes, hidden symmetry and complete integrability

**Abstract: **In physics and mathematics the symmetry allows one to simplify
a problem, and often to make it solvable. According to the
Noether theorem, symmetries are responsible for conservation
laws. Besides evident (explicit) spacetime symmetries,
responsible, for example, for the conservation of energy,
momentum, and angular momentum of a system, there also exist
what is called hidden symmetries, which are connected with
higher order in momentum integrals of motion. A remarkable fact
is that stationary black holes with spherical topology of the
horizon in four and higher dimensions always possess a set
(`tower') of explicit and hidden symmetries which make the
equations of motion of particles and light in their spacetime
completely integrable. The talk gives a general review of the
recently obtained results.

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### Program in Aula Magna

Honorary degree of Doctor of physical-mathematical sciences, honoris causa, will be awarded to

Prof. D. Lynden-Bell, FRS and Prof. Dr. W. Domcke.

*Einstein, Prague and Gravitation*exhibition visit.

Conference participants as well as accompanying persons are invited.

## Wednesday June 27

### Plenary Session in Blue Lecture Hall

**Bernard Schutz**

Gravity talks: observing the Universe with gravitational waves

**Bernard Schutz**

Gravity talks: observing the Universe with gravitational waves

**Abstract: **Einstein's work on gravity was inspired by the need to limit the speed of transmission of gravitational influences to the speed of light, for consistency with special relativity. This leads inevitably to gravitational waves. But the weakness of the waves' interaction with matter has made them hard to detect, so that the first detections are expected in the next few years. By the end of this decade there might be a network of 5 powerful detectors around the world, and a space-based detector might be under construction. When gravity begins to talk back to us, to tell us about strong fields directly through the waves they produce, astronomy will gain a completely new way of gathering information. We will test gravity theory in strong fields, verify directly the existing of horizons, finally learn how often black holes are produced when stars die, study the structure of neutron stars, directly probe the black-hole engines of gamma-ray bursts, and independently measure the rate of expansion of the universe.

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**Daniel Sudarsky**

The quantum gravity interface and the origin of the seeds of cosmic structure during inflation

**Daniel Sudarsky**

The quantum gravity interface and the origin of the seeds of cosmic structure during inflation

**Abstract: **
The observations of the first traces of cosmic structure in the Cosmic Microwave Background are in excellent agreement with the predictions of Inflation. However, as we shall see, that account is not fully satisfactory, as it does not address the transition from an homogeneous and isotropic early stage to a later one lacking those symmetries. We will argue that New Physics is needed to account for such transition and that Quantum Gravity might be the place from where this new physics emerges. Moreover, we will show that the observations can be used to constrain the various phenomenological proposals made in this regard.

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**Helmut Friedrich**

The large scale Einstein evolution problem

**Helmut Friedrich**

The large scale Einstein evolution problem

**Abstract: **Asymptotic considerations do not only play an important role in the interpretation of gravitational fields but also in deriving large scale existence results. With this in mind we revisit certain existence and non-linear stability results for solutions to Einstein's field equations which have been obtained under various assumptions on the matter fields and the sign of the cosmological constant and discuss various questions concerning the specific asymptotic behaviour of the fields, which has been derived or imposed in the different cases.

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**Hermann Nicolai**

Quantum Gravity: the view from particle physics

**Hermann Nicolai**

Quantum Gravity: the view from particle physics

**Abstract: **In this talk I will review some facts and lessons
that particle physics can offer to help in the search for a fully
consistent theory of quantum gravity, including a brief discussion
of recent LHC data from this perspective.

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**John Friedman**

Stability of relativistic stars

**John Friedman**

Stability of relativistic stars

**Abstract: **The stable relativistic stars form a two-dimensional family parametrized by mass and spin. Radial instabilities to collapse and to explosive
expansion set upper and lower limits on their mass; and an instability
driven by gravitational waves may limit on their spin. Gravitational waves
from unstable nonaxisymmetric modes of nascent neutron stars, old stars
spun up by accretion, and the hypermassive remnants of binary mergers, are
all candidates for gravitational wave detectors, but major uncertainties in
the microphysics persist.

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**Gabriela Gonzalez**

Gravitational Wave Astronomy with LIGO and Virgo detectors

**Gabriela Gonzalez**

Gravitational Wave Astronomy with LIGO and Virgo detectors

**Abstract: **I will present the latest results from the searches for gravitational waves in LIGO and Virgo data taken in the last several years, including the results from a blind injection experiment in 2010 on the ability to make a discovery, and on the efforts to search for electromagnetic and high-energy counterparts of gravitational wave triggers. I will also present the status of the Advanced LIGO and Virgo detectors, and review the bright prospects for gravitational wave astronomy with the international network.

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**Gerhard Heinzel**

Low-frequency gravitational wave detectors in space

**Gerhard Heinzel**

Low-frequency gravitational wave detectors in space

**Abstract: **The low-frequency part of the gravitational wave spectrum, from 100 micro-Hertz up to 1 Hz, contains the most spectacular sources of gravitational waves. Really high precision measure-ments are possible here, making this frequency range very interesting for both Astronomy and Fundamental Physics. To open this window for observations, we need an observatory in space!

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### Parallel Session in Blue Lecture Hall

**Andrew Hamilton**

Generalized thermodynamics inside black holes

**Andrew Hamilton**

Generalized thermodynamics inside black holes

**Abstract: **There is persistent and endemic confusion between the true (or future) horizon that an infaller passes when they fall into a black hole, and the illusory (or past) horizon, which is the exponentially redshifted image of the object that collapsed to a black hole long ago. I will use a general relativistically accurate interactive Black Hole Flight Simulator to illustrate the distinction between the true and illusory horizons. I will argue that (it is obvious that): (a) Hawking radiation arises from the illusory horizon, for both inside and outside observers; (b) the entropy of the black hole is a quarter of the area of the illusory horizon, for both inside and outside observers; (c) the illusory horizon is intrintrinsically nonlocal, and is at the root of the nonlocality (information) paradox; (d) when an infaller reaches the singularity, their states merge with the illusory horizon.

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**Maxim Lyutikov**

Hair of astrophysical black holes

**Maxim Lyutikov**

Hair of astrophysical black holes

**Abstract: **The ``no hair'' theorem is not applicable if the black hole is surrounded by highly conducting plasma. Astrophysical black holes formed from the collapse of a
rotating magnetized neutron stars, which can self-produce particles via vacuum
breakdown and form a highly conducting plasma magnetosphere, can keep the effectively ``frozen-in''
magnetic field lines both during and after the collapse.
This introduces a topological constraint which prohibits the open magnetic field lines
from sliding off the newly-formed event horizon. During collapse of a neutron star into the black hole, the latter conserves the number of magnetic flux tubes open to infinity. As a result, an isolated black hole can spin down electromagnetically.

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**Dimitrios Psaltis**

Testing the no-hair theorem with astrophysical black holes

**Dimitrios Psaltis**

Testing the no-hair theorem with astrophysical black holes

**Abstract: **The Kerr spacetime of spinning black holes is one of the most intriguing predictions of Einstein's theory of general relativity. The special role this spacetime plays in the theory of gravity is encapsulated in the no-hair theorem, which states that the Kerr metric is the only realistic black-hole solution of the vacuum field equations. Recent and anticipated advances in the observations of black holes throughout the electromagnetic spectrum have secured our understanding of their basic properties while opening up new opportunities for devising tests of the Kerr metric. In this talk, I will show how imaging and dynamical observations of accreting black-holes with current and future instruments will lead to the first direct test of the no-hair theorem with an astrophysical object. I will also discuss the current state of the Event Horizon Telescope, which will obtain, in the near future, the first horizon-scale image of the black hole in the center of the Milky Way.

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**Georgios Loukes-Gerakopoulos**

Non-linear effects in non-Kerr spacetimes

**Georgios Loukes-Gerakopoulos**

Non-linear effects in non-Kerr spacetimes

**Abstract: **The absence of a Carter-like constant in stationary axisymmetric perturbations of black hole spacetimes allows the appearance of chaos. Although, chaos in frequency analysis corresponds
to noise, certain non-linear effects of these non-integrable systems can be observed. I will present some of these effects and their corresponding imprints on the frequency spectra.

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**Eva Hackmann**

Geodesic equations and algebro-geometric methods

**Eva Hackmann**

Geodesic equations and algebro-geometric methods

**Abstract: **For an investigation of the physical properties of gravitational fields the observation of massive test particles and light is very useful. The characteristic features of a given space-time may be decoded by studying the complete set of all possible geodesic motions. Such a thorough analysis can be accomplished most effectively by using analytical methods to solve the geodesic equation. In this contribution, we will present the use of elliptic functions and their generalizations for solving the geodesic equation in a wide range of well known space-times, which are part of the general Pleba\'nski-Demia\'nski family of solutions. In addition, we address the definition and calculation of observable effects like the perihelion shift and outline further applications of the presented methods.

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**Samuel Gralla**

Second-Order Gravitational Self-Force

**Samuel Gralla**

Second-Order Gravitational Self-Force

**Abstract: **The prospect of gravitational-wave astronomy has renewed interest in the old problem of the motion of a particle taking into account the effects of its self-field. In the context of a small mass described by the theory of general relativity, roughly fifteen years of work has established---and in some cases solved---an equation of motion valid to first order in the size/mass of the body (i.e., taking into account the leading order effects of the self-field). However, for the gravitational-wave application, second-order effects may in fact be required, i.e., it may be necessary to include self-field effects corresponding to non-linear terms in the Einstein equation. I report on recent work, building on previous work with R. Wald at first order, that rigorously derives an equation of motion (in the form of a very complicated prescription!) valid through second-order in the size/mass of a small body. Key elements of the approach at second order are the use of "effective source" techniques to handle the non-linearity and the identification of a class of gauges where a notion of center of mass position may be sensibly defined.

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**Gustavo Dotti**

Gravitational instabilities and cosmic censorship

**Gustavo Dotti**

Gravitational instabilities and cosmic censorship

**Abstract: **I will review the results that we have obtained in the last few years on linear perturbations in the Kerr-Newman family. It is proved that the naked singularities arising in the super-extreme (charge or angular momentum larger than mass) cases are unstable, and that the stationary regions beyond the inner horizon of black holes are also unstable. These results have implications on cosmic censorship in both its weak and strong forms, since the inner horizon is also a Cauchy horizon for an appropriate data surface on the black hole exterior.
The dynamics of gravitational perturbations in these non globally hyperbolic spacetimes can be uniquely defined in terms of data on a partial Cauchy surface thanks to the fact that there is a single choice of boundary conditions at the singularity that makes the linear scheme self consistent.

References: Class.Quant.Grav in press; ibid v. 27 (2010) 187005; ibid v. 26 (2009) 215002; ibid v.25 (2008) 2450012; ibid v. 26 (2006) 5063; Phys.Lett. B644 (2007) 289

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### Parallel Session in Red Lecture Hall

**Roberto Sussman**

The averaging problem in Szekeres dust models

**Roberto Sussman**

The averaging problem in Szekeres dust models

**Abstract: **We consider a general formalism of scalar averaging for the study of the dynamics of Szekeres dust models. Although these models do not admit (in general) Killing vectors, their averaged scalars behave as spherically symmetric quantities. We show that under a suitable choice of an invariant weight factor the averaged scalars identically satisfy FLRW dynamics, so that inhomogeneity becomes encoded in their fluctuations. The evolution equations for these averaged scalars and their fluctuations leads to a fully consistent and complete 3-dimensional dynamical system that can be studied with standard techniques. These evolution equations lack the "back-reaction" terms that characterize Buchert's formalism (the average with unit weight factor), and lead in a natural way to define a rigorous perturbation formalism. The main curvature and kinematic invariant scalars are directly related to the variance and covariance momenta constructed with the fluctuations, which leads to a potentially useful and invariant definition of gravitational entropy.

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**David Wiltshire**

What is dust? Coarse graining, cosmic variance and cosmic expansion

**David Wiltshire**

What is dust? Coarse graining, cosmic variance and cosmic expansion

**Abstract: **When Einstein first applied his field equations to cosmology he imagined a universe of stellar density, in which the energy-momentum tensor averages only over nongravitational forces. Nearly 100 years later we observe a universe which is only homogeneous in a statistical sense on scales larger than 100/h Mpc. To coarse-grain dust on these scales requires us to coarse-grain the gravitational degrees of freedom themselves. This necessitates a re-examination of foundational questions relating to the nonlocalizability of gravitational energy; issues which vexed Einstein as he struggled towards general relativity 100 years ago. I argue that a re-examination of these issues has immediate observable consequences. Indeed, a detailed study of 4,534 redshifts and distances in a model-independent manner (arXiv:1201.5371) has led us to the suggestion that the CMB dipole is partly due to a 0.6% anisotropy in the distance-redshift relation due to foreground structures on scales up to 65/h Mpc, which can only be understood as the differential expansion of space rather than as Newtonian velocity perturbations on a fixed homogeneous background. This result, if true, will have profound consequences for cosmology.

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**Nelson Pinto-Neto**

The quantum-to-classical transition of primordial cosmological perturbations

**Nelson Pinto-Neto**

The quantum-to-classical transition of primordial cosmological perturbations

**Abstract: **There is a widespread belief that the classical small inhomogeneities which gave rise to all structures in the Universe through gravitational instability originated from primordial quantum cosmological fluctuations. However, this transition from quantum to classical fluctuations is plagued with important conceptual issues, most of them related to the application of standard quantum theory to the Universe as a whole. In this paper, we show how these issues can easily be overcome in the framework of the de Broglie-Bohm quantum theory. This theory is an alternative to standard quantum theory that provides an objective description of physical reality, where rather ambiguous notions of measurement or observer play no fundamental role, and which can hence be applied to the Universe as a whole. In addition, it allows for a simple and unambiguous characterization of the classical limit.

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**Saulo Carneiro**

A cosmological concordance model with particle creation

**Saulo Carneiro**

A cosmological concordance model with particle creation

**Abstract: **We show that creation of dark-matter particles at a constant rate implies the existence of a vacuum term that decays linearly with the Hubble rate. We discuss the cosmological model that arises in this context and test it against observations of the first acoustic peak in the cosmic microwave background (CMB) anisotropy spectrum, the Hubble diagram for supernovas of type Ia (SNIa), the distance scale of baryonic acoustic oscillations (BAO) and the distribution of large scale structures. We show that a good concordance is obtained, albeit with a higher value of the present matter abundance than in the standard model.

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**Julien Larena**

A cosmological lattice model

**Julien Larena**

A cosmological lattice model

**Abstract: **We study a cosmological model consisting of an infinite number of masses M placed on a cubic lattice of size L. The purpose of the study is to obtain a toy-model for a Universe made of localized masses, in order to test the usual fluid approximation of cosmology, as well as the Lindquist-Wheeler tesselated approximation that has recently been employed to explore the possibility to replace Dark Energy by an effect of inhomogeneities.
We find a solution that is exact at order M/L, thus representing adequately a lattice of galactic-size objects separated by inter-galactic distances. The kinematics of the solution matches exactly the one of the corresponding Friedmann-Lemaitre-Robertson-Walker (FLRW) model with a dust matter component having the equivalent energy density. This supports the fluid approximation.
Nevertheless, differences arise in the propagation of light and the values of observables, between the lattice model and the kinematically equivalent smoothed one. We comment on these effects and their potential observability, and we compare our results to the ones obtained in Wheeler-Lindquist models and in the FLRW context when using the Dyer-Roeder equation to take into account the clumping of matter.

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**Giovanni Marozzi**

Backreaction effects on the luminosity-redshift relation in inhomogeneous cosmology

**Giovanni Marozzi**

Backreaction effects on the luminosity-redshift relation in inhomogeneous cosmology

**Abstract: **I will show a general gauge invariant formalism for defining
cosmological averages that are relevant for observations based on
light-like signals. Such averages involve either null hypersurfaces
corresponding to a family of past light-cones or compact surfaces
given by their intersection with timelike hypersurfaces. Afterwards,
using such formalism, together with adapted "geodesic light-cone"
coordinates, I will show as backreaction effect emerges in the
evaluation of the luminosity distance-redshift relation in an inhomogeneous Universe. To conclude, considering a realistic stochastic spectrum of
inhomogeneities of primordial (inflationary) origin, I will show
the magnitude and behaviour of such backreaction effects.

Talk based on the following papers:
M. Gasperini, G. Marozzi, F. Nugier and G. Veneziano, JCAP 1107, 008 (2011), arXiv:1104.1167 [astro-ph.CO];
I. Ben-Dayan, M. Gasperini, G. Marozzi, F. Nugier and G. Veneziano, arXiv:1202.1247 [astro-ph.CO];
I. Ben-Dayan, M. Gasperini, G. Marozzi, F. Nugier and G. Veneziano, in preparation.

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**Phillip Helbig**

Is there a flatness problem in classical cosmology?

**Phillip Helbig**

Is there a flatness problem in classical cosmology?

**Abstract: **I briefly review the flatness problem within the context of classical
cosmology and examine some of the debate in the literature with regard
to its definition and even the question whether it exists. I then
present some new calculations for cosmological models which will
collapse in the future; together with previous work by others for models
which will expand forever, this allows one to examine the flatness
problem quantitatively for all cosmological models. This leads to the
conclusion that the flatness problem does not exist, not only for the
cosmological models corresponding to the currently popular values of
$\lambda_0$ and $\Omega_0$ but indeed for all Friedmann-Lema\^itre
models.

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### Parallel Session in Yellow Lecture Hall

**Alejandro Corichi**

Effective Dynamics of Anisotropic Cosmologies in Loop Quantum Cosmology

**Alejandro Corichi**

Effective Dynamics of Anisotropic Cosmologies in Loop Quantum Cosmology

**Abstract: **We present results of numerical evolutions of effective equations for anisotropic cosmologies with spatial curvature in loop quantum cosmology. We address the issue of singularity resolution for different types of initial conditions and study the behavior of geometrical scalar quantities.

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**Steffen Gielen**

Spontaneous breaking of Lorentz symmetry for canonical gravity

**Steffen Gielen**

Spontaneous breaking of Lorentz symmetry for canonical gravity

**Abstract: **In Hamiltonian formulations of general relativity, in particular Ashtekar variables which serve as the classical starting point for loop quantum gravity, Lorentz covariance is a subtle issue which has been the focus of some debate, while at the same time being crucial with regard to possible experimental tests. After reviewing the sources of difficulty, we present a Lorentz covariant formulation in which we generalise the notion of a foliation of spacetime usually used in the Hamiltonian formalism to a field of ”local observers” which specify a time direction only locally. This field spontaneously breaks the local SO(3,1) symmetry down to a subgroup SO(3), in a way similar to systems in condensed matter and particle physics. The formalism is analogous to that in MacDowell-Mansouri gravity, where SO(4,1) is spontaneously broken to SO(3,1). We show that the apparent breaking of SO(3,1) to SO(3) is not in conflict with Lorentz covariance. We close by outlining other possible applications of the formalism of local observer, especially with regard to phenomenology of quantum gravity.

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**Thomas Roman**

Probability Distributions of Quantum Stress Tensors in Two and Four Dimensions

**Thomas Roman**

Probability Distributions of Quantum Stress Tensors in Two and Four Dimensions

**Abstract: **This talk discusses recent work with Chris Fewster and Larry Ford on probability distributions
for smeared quantum fields in the vacuum in two and four-dimensional Minkowski spacetime.
These distributions have the feature that there is a lower bound at a finite negative value,
but no upper bound. The lower bound of the distribution gives the optimal quantum inequality
bound, thus illustrating a deep connection between these probability distributions and
quantum inequalities. However, arbitrarily large positive energy density fluctuations are
possible. In two dimensions, the unique exact analytic form for the distribution has been
found for the stress tensor of a massless scalar field in the vacuum state. In four dimensions,
we are not able to give closed form expressions for the probability distribution, but rather use
calculations of a finite number of moments to estimate the lower bounds, the asymptotic
forms for large positive argument, and possible fits to the intermediate region.
All of our four-dimensional results are subject to the caveat that these distributions
are not uniquely determined by the moments. We apply the asymptotic form of the electromagnetic energy density
distribution to estimate the nucleation rates of black holes and of Boltzmann brains.

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**Florian Girelli**

Geometric operators in loop quantum gravity with a cosmological constant

**Florian Girelli**

Geometric operators in loop quantum gravity with a cosmological constant

**Abstract: **Loop quantum gravity is a candidate to describe the quantum gravity regime with zero cosmological constant. One of its key results is that geometric operators, such as area, angle, volume, are quantized. Not much is known when the cosmological constant is not zero. It is usually believed that to introduce this parameter in the game, we need to use quantum groups. However due to the complicated algebraic structure inherent to quantum groups not much is known in this case. Apart from the area operator, the geometric operators are not yet defined. I will discuss how the use of tensor operators can circumvent the difficulties and allow to construct a natural set of observables. In particular, I will construct the natural geometric observables such as angle or volume and discuss some of their properties.

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**Manuel Krämer**

Can effects of quantum gravity be observed in the cosmic microwave background?

**Manuel Krämer**

Can effects of quantum gravity be observed in the cosmic microwave background?

**Abstract: **We investigate the question whether small quantum-gravitational effects can be observed in the anisotropy spectrum of the cosmic microwave background radiation. An observation of such an effect is needed in order to discriminate between different approaches to quantum
gravity. Using canonical quantum gravity with the Wheeler-DeWitt equation, we find a suppression of power at large scales. Current observations only lead to an upper bound on the energy scale of inflation, but the framework is general enough to study other situations in which such effects might indeed be seen.

Reference: C. Kiefer and M. Krämer, Quantum Gravitational Contributions to the Cosmic Microwave Background Anisotropy Spectrum, Phys. Rev. Lett. 108, 021301 (2012).

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**Franz Hinterleitner**

Quantization of plane gravitational waves

**Franz Hinterleitner**

Quantization of plane gravitational waves

**Abstract: **A long-standing problem in Loop Qauntum Gravity (LQG) is the semiclassical limit and the question of Lorentz invariance violation due to the "granularity" of quantum space-time. In full 3+1 LQG there are strong indications for such violations, but no definitve answer to this issue has been given so far.

Unidirectional plane gravitational waves are 1+1 dimensional fully general-relativistic systems, which are convenient for an investigation of possible dispersion of gravitational radiation, quantum fluctuations of flat space, and the speed of light in a quantum space-time environmant.

In a recent paper a classical canonical approach to plane waves was found, where the reduction from arbitrarily forth- and back running waves to unidirectional ones is formulated in terms of first-class constraints. This means that this step of symmetry reduction can be carried out after quantization. The presently ongoing work deals with the formulation of the corresponding quantum constraint operators and the construction of solutions.

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**Lee Hodgkinson**

Static, stationary and inertial Unruh-DeWitt detectors on the BTZ black hole

**Lee Hodgkinson**

Static, stationary and inertial Unruh-DeWitt detectors on the BTZ black hole

**Abstract: **We examine an Unruh-DeWitt particle detector coupled to a scalar field
in three-dimensional curved spacetime. We first obtain a
regulator-free expression for the transition probability in an
arbitrary Hadamard state, working within first-order perturbation
theory and assuming smooth switching, and we show that both the transition
probability and the instantaneous transition rate remain well-defined and
finite in the sharp switching limit. We then analyse the detector for
a massless conformally coupled field in the Hartle-Hawking vacua on the
Ba\~nados-Teitelboim-Zanelli black hole, under both transparent and reflective boundary
conditions. A~selection of stationary and freely-falling detector
trajectories are examined, including the co-rotating trajectories, for
which the response is shown to be thermal. Analytic results in a
number of asymptotic regimes, including those of large and small mass,
are complemented by numerical results in the interpolating regimes. The
boundary condition at infinity is seen to have a significant effect on
the detector.

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### Public Lecture

**Michael Kramer**:

*Was Einstein Right? – How cosmic time keepers in space probe Einstein's strange world*

Public lecture in the Great Lecture Hall of the Faculty of Arts of Charles University.

## Thursday June 28

### Plenary Session in Blue Lecture Hall

**Thibault Damour**

The Two-Body Problem in General Relativity

**Thibault Damour**

The Two-Body Problem in General Relativity

**Abstract: **The two-body problem has a long history in General Relativity.
It has recently acquired a renewed practical importance in view
of the development of interferometric detectors of gravitational waves.
Indeed, a network of ground-based interferometric gravitational wave detectors
(LIGO/VIRGO...) is currently being upgraded, and should, in a few years,
reach a sensitivity enabling them to detect the gravitational waves emitted
by coalescing compact binaries: i.e. binary systems made of black holes and/or
neutron stars. This prospect has motivated renewed theoretical studies of the
motion and radiation of relativistic two-body systems. I will review the recent
analytical studies of (comparable-mass) two-body systems, and their comparison to numerical
relativity results. Particular attention will be given to the recently
developed "effective one body" approach to the motion and radiation of
binary systems.

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**Gerhard Schäfer**

Hamiltonian formalism of spinning black holes in general relativity

**Gerhard Schäfer**

Hamiltonian formalism of spinning black holes in general relativity

**Abstract: **The mathematical treatment of the motion and spin precession of
selfgravitating spinning compact objects in general relativity is manageable
to the order linear in spin with the aid of the Tulczyjew stress-energy tensor
in pole-dipole approximation, also applying regularization techniques.
In my talk a Hamilton canonical treatment of gravitationally interacting
spinning black holes will be presented using a tetrad-generalization of the
Arnowitt-Deser-Misner canonical formulation of general relativity. The
formalism is valid through linear order in the single spins. For binary
systems, higher-order post-Newtonian Hamiltonians will be given in explicit
analytic form. Higher order in spin generalizations will be discussed too.

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**Luciano Rezzolla**

Using numerical relativity to explore fundamental physics and astrophysics

**Luciano Rezzolla**

Using numerical relativity to explore fundamental physics and astrophysics

**Abstract: **Recent years have seen a major progress in numerical relativity and the solution of the simplest and yet among the most challenging problems in classical general relativity: that of the evolution of two objects interacting only gravitationally. I will review the results obtained so far when modelling binaries of black holes or of neutron stars and also discuss the impact these studies have in detection of gravitational-waves, in astrophysics, and in our understanding of general relativity.

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**Jerzy Lewandowski**

Loop Quantum Gravity - where are we?

**Jerzy Lewandowski**

Loop Quantum Gravity - where are we?

**Abstract: **For several models of gravity coupled to other fields, the
algorithm of the canonical quantization has been completed and performed
to an end. It gave rise to well defined, exact quantum theories. The
Dirac observables are provided by the relational and the deparametrization
frameworks. The quantum states, Hilbert spaces and concrete quantum
operators are furnished by the canonical Loop Quantum Gravity framework.
The models are not confirmed experimentally and admit ambiguities, but
they are there, available for further study and applications.

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**Leor Barack**

Gravitational self-force: orbital mechanics beyond the geodesic approximation

**Leor Barack**

Gravitational self-force: orbital mechanics beyond the geodesic approximation

**Abstract: **The fundamentally simple question of motion in a gravitationally-bound two-body system is a longstanding open problem of General Relativity. When the mass ratio is large the problem lends itself to a perturbative treatment, whereby corrections to the geodesic motion of the smaller object (due to radiation reaction, internal structure, etc.) are accounted for order by order in a small-mass-ratio expansion, using the language of an effective ``gravitational self-force''. The prospect for observing gravitational waves from compact objects inspiralling into massive black holes in the foreseeable future has in the past 15 years motivated a program to obtain a rigorous formulation of the self-force and compute it for astrophysically interesting systems. I will begin this talk by reviewing the general theory of the gravitational self-force in curved spacetime, and proceed to describe how this theory is being implemented today in actual calculations of the self force for inspiral orbits. I will discuss recent calculations of some conservative post-geodesic effects of the self-force (including the finite-mass correction to the precession rate of the periastron), and highlight the way in which these calculations allow us to make a fruitful contact with post-Newtonian theory and with Numerical Relativity, and also inform the development of a universal Effective One Body model of the two-body dynamics.

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**Andrzej Rostworowski**

Instability of anti de-Sitter spacetime

**Andrzej Rostworowski**

Instability of anti de-Sitter spacetime

**Abstract: **In a joint work with Piotr Bizoń, we study the nonlinear evolution of a weakly perturbed anti-de Sitter (AdS) space by solving numerically the spherically symmetric Einstein-massless-scalar field equations with a negative cosmological constant. Our results suggest that AdS spacetime is unstable against a black hole formation under arbitrarily small generic perturbations. We conjecture that this instability is triggered by a resonant mode mixing which gives rise to diffusion of energy from low to high frequencies. A partial summary of our results can be found in Phys.Rev.Lett 107 031102 [arXiv:1104.3702].

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### Afternoon program

**Tour**'Old Prague Physical and Astronomical'

**Organ concert**in St. Vitus Catedral

**Conference banquet**in the foundry of Emperor Rudolph II located at Prague Castle

## Friday June 29

### Plenary Session in Blue Lecture Hall

**Andrew Hamilton**

Interactive Black Hole Flight Simulation

**Andrew Hamilton**

Interactive Black Hole Flight Simulation

**Abstract: **A real-time interactive Black Hole Flight Simulator will be used to demonstrate the appearance of a black hole as seen by observers on geodesics both outside and inside the horizon.

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**Gernot Neugebauer**

Stationary two-black-hole configurations: A non-existence proof for disconnected horizons

**Gernot Neugebauer**

Stationary two-black-hole configurations: A non-existence proof for disconnected horizons

**Abstract: **We resume former discussions of the question, whether the spin-spin repulsion and the gravitational attraction of two aligned black holes can balance each other. Based on the solution of a boundary problem for disconnected (Killing) horizons and the resulting violation of characteristic black hole properties, we present a non-existence proof for the equilibrium configuration in question. From a mathematical point of view, this result is a further example for the efficiency of the inverse (´scattering´) method in non-linear theories.

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**Lars Andersson**

Cosmological models and stability

**Lars Andersson**

Cosmological models and stability

**Abstract: **In this talk I will discuss some mathematical results on
inhomogeneous cosmological models, focusing on late time behavior and
the issues of nonlinear stability versus instability.

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**Robert Wald**

Stability of Black Holes and Black Branes

**Robert Wald**

Stability of Black Holes and Black Branes

**Abstract: **I describe recent work with Stefan Hollands (arXiv:1201.0463) that
establishes a close relationship between dynamical stability and
thermodynamic stability for black holes and black branes in classical
general relativity in spacetime dimensions $D \geq 4$. We show that for
axisymmetric perturbations of an arbitrary stationary, axisymmetric black
hole, dynamical stability is equivalent to the positivity of canonical
energy of perturbations that have vanishing linearized ADM mass and
angular momentum at infinity. We further show that positivity of canonical
energy is equivalent to thermodynamic stability. A thermodynamically
unstable black hole may be dynamically stable (as is the case for a
Schwarzschild black hole) if the only perturbations with negative
canonical energy have nonvanishing linearized mass and/or angular
momentum. However, we show that all black branes associated with
thermodynamically unstable black holes must be dynamically unstable, as
conjectured by Gubser and Mitra. We also prove that positivity of
canonical energy for perturbations with vanishing linearized mass and
angular momentum is equivalent to the satisfaction of a "local Penrose
inequality," thus showing that satisfaction of this local Penrose
inequality is necessary and sufficient for dynamical stability. Although
we explicitly consider vacuum general relativity, most of our results are
derived using general Lagrangian and Hamiltonian methods and therefore can
be generalized to allow for the presence of matter fields and/or to the
case of an arbitrary diffeomorphism covariant gravitational action.

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**Marc Mars**

Stability of marginally outer trapped surfaces and geometric inequalities

**Marc Mars**

Stability of marginally outer trapped surfaces and geometric inequalities

**Abstract: **Marginally outer trapped surfaces (MOTS) admit
a notion of stability that in many respects generalizes a
similar notion for minimal hypersurfaces. Stable MOTS
play an interesting role in a number of geometric inequalities
involving physical parameters such as area, mass, charge or, in the
axially symmetric case, angular momentum. Some of those
inequalities are global in nature while others are local, with
interesting relationships between them.
In this talk I will introduce the notion of stable MOTS
and describe some of the geometric inequalities conjectured for them.

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**Donato Bini**

Observers, observables and measurements in general relativity

**Donato Bini**

Observers, observables and measurements in general relativity

**Abstract: **The definition of special observers and frames, geometrically or physically motivated, is discussed. Applications to black hole spacetimes and other astrophysically relevant contexts are also presented.

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### Parallel Session in Blue Lecture Hall

**Tim Koslowski**

Shape Dynamics

**Tim Koslowski**

Shape Dynamics

**Abstract: **Shape Dynamics is a reformulation of General Relativity where refoliation invariance is traded for local spatial conformal invariance. This is an example of the concept of equivalence of Hamiltonian gauge theories, where two theories are called equivalent if and only if each can be gauged such that in these two particular gauges the two theories admit identical initial value problems and identical equations of motion. The BRST formulation of this duality suggests a novel definition of gravity theories, in particular in the effective field theory framework.

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**Hideki Maeda**

Exact dynamical AdS black holes and wormholes with a Klein-Gordon field

**Hideki Maeda**

Exact dynamical AdS black holes and wormholes with a Klein-Gordon field

**Abstract: **We present a set of exact solutions in the Einstein-Klein-Gordon system with a cosmological constant in arbitrary dimensions.
The spacetime has spherical, plane, or hyperbolic symmetry and a class of solutions represents an asymptotically locally AdS dynamical black hole or wormhole.
In four and higher dimensions, the quasi-local mass blows up at the AdS infinity, suggesting that the slow fall-off is realized.
In three dimensions, the scalar field becomes trivial and the solution reduces to the BTZ black hole.

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**David Kubiznak**

On integrability of spinning particle motion in higher-dimensional rotating black hole spacetimes

**David Kubiznak**

On integrability of spinning particle motion in higher-dimensional rotating black hole spacetimes

**Abstract: **In this talk, I shall review several various approaches for describing a spinning particle in curved rotating black hole background and discuss their `integrability properties'. In particular, I will concentrate on a semiclassical theory, where the spin degrees of freedom are described by a vector of Grassmann variables. I will show that for rotating black hole spacetimes in any dimension n there exist n bosonic functionally independent integrals of spinning particle motion, corresponding to explicit and hidden symmetries generated from the principal Killing-Yano tensor. Moreover, in 4, 5, 6, and 7 dimensions such integrals are in involution, making the bosonic part of the motion integrable. This is conjectured to be valid in any dimension. The presented construction generalizes the result of Page et. al. [hep-th/0611083] on complete integrability of geodesic motion in these spacetimes.

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**Alena Pravdová**

On the Goldberg-Sachs theorem in five dimensions

**Alena Pravdová**

On the Goldberg-Sachs theorem in five dimensions

**Abstract: **We discuss generalization of the Godlberg-Sachs theorem to higher dimensions. After working out some general constraints that hold in arbitrary dimensions, we determine necessary algebraic conditions on the optical matrix of a multiple WAND in a five-dimensional Einstein spacetime. We prove that there are three canonical classes of the optical matrices. We provide explicit examples of spacetimes corresponding to each form discussed.

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**Andres Anabalon**

Exact Black Holes and Universality in the Backreaction of non-linear Sigma Models with a potential in (A)dS4

**Andres Anabalon**

Exact Black Holes and Universality in the Backreaction of non-linear Sigma Models with a potential in (A)dS4

**Abstract: **The aim of the talk is to describe the construction of accelerated, stationary and axisymmetric exact solutions of the Einstein theory with self interacting scalar fields in (A)dS4. To warm up, the backreaction of the (non)-minimally coupled scalar field is solved, the scalar field equations are integrated and all the potentials compatible with the metric ansatz and Einstein gravity are found. With these results at hand the non-linear sigma model is tackled. The scalar field Lagrangian is generic; neither the coupling to the curvature, neither the metric in the scalar manifold nor the potential, are fixed ab initio. The unique assumption in the analysis is the metric ansatz: it has the form of the most general Petrov type D vacuum solution of general relativity; it is a a cohomogeneity two Weyl rescaling of the Carter metric and therefore it has the typical Plebanski-Demianski form with two arbitrary functions of one variable and one arbitrary functions of two variables. It is shown, by an straightforward manipulation of the field equations, that the metric is completely integrable without necessity of specifiying anything in the scalar Lagrangian. This results in that the backreaction of the scalar fields, within this class of metrics, is universal. The metric functions generically show an explicit dependence on a dynamical exponent that allows to smoothly connect this new family of solutions with the actual Plebanski-Demianski spacetime. The remaining field equations imply that the scalar fields follow geodesics in the scalar manifold with an affine parameter given by a non-linear function of the spacetime coordinates and define the on-shell form of the potential plus a functional equation that it has to satisfy. Finally, a general family of (A)dS4 static hairy black holes is explicitly constructed and its properties are outlined.

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**Andrei Zelnikov**

Self-energy of a scalar charge near higher-dimensional black holes

**Andrei Zelnikov**

Self-energy of a scalar charge near higher-dimensional black holes

**Abstract: **We study the problem of self-energy of charges in higher dimensional static spacetimes. Application of regularization methods of quantum field theory to calculation of the classical self-energy of charges leads to model-independent results. The correction to the self-energy of a scalar charge due to the gravitational field of black holes of the higher dimensional Majumdar-Papapetrou spacetime is calculated exactly. It proves to be zero in even dimensions, but it acquires non-zero value in odd dimensional spacetimes.

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**Jiří Podolský**

Geodesic deviation in Kundt spacetimes of any dimension

**Jiří Podolský**

Geodesic deviation in Kundt spacetimes of any dimension

**Abstract: **Using the invariant form of equation of geodesic deviation, that describes relative motion of free test particles, we investigate a completely general family of $D$-dimensional Kundt spacetimes. We demonstrate that local influence of the gravitational field can be naturally decomposed into Newton-type tidal effects typical for type~II spacetimes, longitudinal deformations mainly present in spacetimes of algebraic type~III, and type~N purely transverse effects corresponding to gravitational waves with $D(D-3)/2$ independent polarization states. We also explicitly study the most important examples, namely exact pp-waves, gyratons, and VSI spacetimes. This analysis helps us to clarify the geometrical and physical interpretation of the Kundt class of nonexpanding, nontwisting, and shearfree geometries.

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**Marco Cariglia**

Dirac equation in curved spacetime and hidden symmetries

**Marco Cariglia**

Dirac equation in curved spacetime and hidden symmetries

**Abstract: **I will discuss the importance of hidden symmetries in the study of the Dirac equation curved spacetime. Conformal Killing-Yano special tensors are associated to symmetries of the Dirac equation, and in some notable cases like the higher dimensional Kerr-NUT-(A)dS black holes lead to full separation of variables. I will discuss in this case how the symmetries operators can be simultaneously diagonalised. Conformal Killing-Yano tensors and their related symmetry operators admit a generalisation in the case of metrics with fluxes that are of relevance for supergravity theories. Finally, if time permits I will mention the Eisenhart lift of a spacetime and its relation to the Dirac equation.

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### Parallel Session in Red Lecture Hall

**Balasubramanian Iyer**

The 2.5PN linear momentum flux and associated recoil from inspiralling compact binaries in quasi-circular orbits: Nonspinning case

**Balasubramanian Iyer**

The 2.5PN linear momentum flux and associated recoil from inspiralling compact binaries in quasi-circular orbits: Nonspinning case

**Abstract: **Anisotropic emission of gravitational-waves (GWs) from inspiralling compact binaries leads to the loss of linear momentum and gravitational recoil of the system. The loss rate of linear momentum for a non-spinning binary system of black holes in quasi-circular orbit is obtained at the 2.5 post-Newtonian (PN) order and used to provide an analytical expression for the 2.5PN accurate recoil velocity of the binary in the inspiral phase. The maximum recoil velocity of the binary system at the innermost stable circular orbit (ISCO)) estimated by the 2.5PN formula is of the order of 4 km/s which is smaller than the 2PN estimate of 22 km/s. This indicates the importance of higher order post-Newtonian (PN) corrections. Going beyond inspiral, we provide an estimate of the more important contribution to the recoil velocity from the plunge phase. The maximum recoil velocity at the end of the plunge, involving contributions both from inspiral and plunge phase, for a binary with symmetric mass ratio $\nu=0.2$ is of the order of 182 km/s.

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**James Nester**

A reference for the covariant Hamiltonian boundary term

**James Nester**

A reference for the covariant Hamiltonian boundary term

**Abstract: **The Hamiltonian for dynamic geometry generates the evolution
of a spatial region along a vector field. It includes a boundary term
which determines both the value of the Hamiltonian and the boundary
conditions. The value gives the quasi-local quantities:
energy-momentum, angular-momentum/center-of-mass. The boundary term
depends not only on the dynamical variables but also on their
reference values, the latter determine the ground state (having
vanishing quasi-local quantities). For our preferred boundary term for
Einstein's GR we propose 4D isometric matching and extremizing the
energy to determine the reference metric and connection values.

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**Laszlo Szabados**

Mass, gauge conditions and spectral properties of the Sen-Witten operator in closed universes

**Laszlo Szabados**

Mass, gauge conditions and spectral properties of the Sen-Witten operator in closed universes

**Abstract: **A non-negative expression, built from the norm of the 3-surface twistor operator and the energy-momentum tensor of the matter fields on a spacelike hypersurface, is found which in the asymptotically flat/hyperboloidal case povides a lower bound for the ADM/Bondi-Sachs mass, while on closed hypersurfaces gives the first eigenvalue of the Sen-Witten operator. Also in the closed case, its vanishing is equivalent to the existence of non-trivial solutions of Witten's gauge condition. Moreover, it is vanishing if and only if the closed data set is in a flat spacetime with spatial topology $S^1\times S^1\times S^1$. Thus, it provides a positive definite measure of the strength of the gravitational field (with physical dimension mass) on closed hypersurfaces, i.e. some sort of the total mass of closed universes. Reference: Class. Quantum Grav. 29 (2012) 095001, or arXiv:1112.2966v2[gr-qc]

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**Michael Jasiulek**

Novel geometric methods for quasi-local mass and spin via isometric embeddings and curvature invariants

**Michael Jasiulek**

Novel geometric methods for quasi-local mass and spin via isometric embeddings and curvature invariants

**Abstract: **Quasi-local mass and angular momentum of bounded regions in numerical binary black hole (BBH) simulations provide necessary information to assemble complete waveforms of BBH inspirals, since the system parameters of the post-Newtonian part and the fully relativistic part of the waveform have to agree.

Meaningful definitions of quasi-local mass and spin are typically based on non-linear elliptic conditions on the geometry and location of closed 2-surfaces in an ambient spatial 3-slice, in order to fix certain gauge freedoms.

To access quasi-local mass of arbitrary bounded regions in numerical relativistic simulation we introduce a novel geometric method to find the isometric embedding of a 2-surface in Euclidean three space through linearised embedding flow which is necessary to determine the Liu-Yau or Brown-York masses.

To access quasi-local mass and angular momentum of axial black hole horizons we introduce a method to read off angular momentum and higher multipole moments through invariant curvature averages. The method does not require a solution of the Killing equation and yields well-defined generalised axial multipole moments for perturbed axial 2-metrics by averaging the contained axial information.

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**István Rácz**

Superradiance or total reflection?

**István Rácz**

Superradiance or total reflection?

**Abstract: **The evolution of a massless scalar field on Kerr background is considered. In particular, the time evolution of initial data specifications with compact support in the distant region is investigated. The inward sent wave packet is tuned to maximize the effect of superradiance. Evidences are shown indicating that instead of the occurrence of energy extraction from black hole the inward sent radiation fail to reach the ergoregion rather it suffers total reflection.

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**Gyula Fodor**

Scalar fields on anti-de Sitter background

**Gyula Fodor**

Scalar fields on anti-de Sitter background

**Abstract: **Because of the implication of anti-de Sitter spacetime instability, there has been much interest recently in scalar fields coupled to gravity when there is a negative cosmological constant. It is an interesting question how different the scalar field evolution is when the background is a fixed AdS metric. On the other hand, it is known that self-interacting massive real scalar fields on flat Minkowski background can form long living oscillating localized objects, called oscillons. In the flat background case these objects radiate energy extremely slowly, in a rate which is exponentially suppressed in terms of the central amplitude. As a result their oscillation frequency slowly increases. On AdS background the situation is different, because then there are localized exactly time-periodic solutions for massive or massless linear Klein-Gordon fields. In my talk I plan to discuss the influence of the AdS background on the structure and stability of oscillons.

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**Cecilia Chirenti**

Quasinormal modes from a naked singularity

**Cecilia Chirenti**

Quasinormal modes from a naked singularity

**Abstract: **What should be the quasinormal modes associated with a spacetime that contains a naked singularity instead of a black hole? In the present work we address this problem by studying the scattering of scalar waves on a curved background described by a Reissner-Nordstr\"om spacetime with $q > m$. We show that there is a qualitative difference between cases with $1 < q^2/m^2 < 9/8$ and cases with $q^2/m^2 > 9/8$. We discuss the necessary conditions for the well-posedness of the problem, and present results for the low $\ell$ and large $\ell$ limits.

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**Marcelo Salgado**

f(R) cosmology revisited

**Marcelo Salgado**

f(R) cosmology revisited

**Abstract: **I shall present various results concerning the analysis of several f(R) models in a FRW spacetime. The analysis is based on an approach where the f(R) theory is not mapped to a Scalar-Tensor Theory in order to avoid the use of potentials that may be ill defined (e.g multivalued). Thus, the Ricci scalar itself is one of the fundamental variables instead of the scalar f'(R). The system of equations is then solved numerically as an initial value problem constrained by the modified-gravity Hamiltonian. This in turn is used to monitor the accuracy of the numerical integration at every time step. Among the results I shall present are the behaviour of the matter-dominated and accelerated eras, the age of the Universe and the confrontation with SNIa data. I intend to discuss the differences and similarities of our findings relative to previous results.

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### Parallel Session in Yellow Lecture Hall

**Alexandre Le Tiec**

The first law of binary black hole mechanics

**Alexandre Le Tiec**

The first law of binary black hole mechanics

**Abstract: **First laws of black hole mechanics, or thermodynamics, come in a variety of different forms. We establish a first law of mechanics for binary systems of point masses moving along circular orbits. This relation is derived from first principles in General Relativity, and is explicitly shown to hold up to very high orders in the post-Newtonian approximation. Analogies are drawn with the single and binary black hole cases, revealing intriguing formal relations between point masses and black holes. Several applications to gravitational-wave source modeling are discussed, such as the computation of the binding energy E and total angular momentum J of the binary system, at leading order beyond the test-particle approximation. The resulting expression for the coordinate invariant relation E(J) is shown to agree remarkably well with the exact results from recent numerical simulations of comparable-mass non-spinning black hole binaries.

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**Enrico Barausse**

The complete non-spinning effective-one-body metric at linear order in the mass ratio

**Enrico Barausse**

The complete non-spinning effective-one-body metric at linear order in the mass ratio

**Abstract: **Using the results of related work, in which the binding energy of a circular-orbit non-spinning compact binary system is computed at leading-order beyond the test-particle approximation, the exact expression of the effective-one-body (EOB) metric component $g^{eff}_{tt}$ is obtained through first order in the mass ratio. Combining these results with the recent gravitational self-force calculation of the periastron advance for circular orbits in the Schwarzschild geometry, the EOB metric component $g^{eff}_{rr}$ is also determined at linear order in the mass ratio. These results assume that the mapping between the real and effective Hamiltonians at the second and third post-Newtonian (PN) orders holds at all PN orders. Our findings also confirm the advantage of resumming the PN dynamics around the test-particle limit if the goal is to obtain a flexible model that can smoothly connect the test-mass and equal-mass limits.

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**Miguel Zilhão**

Dynamics of black holes in de Sitter spacetimes

**Miguel Zilhão**

Dynamics of black holes in de Sitter spacetimes

**Abstract: **We report on the first dynamical evolutions of black holes in asymptotically de Sitter spacetimes. We focus on the head-on collision of equal mass binaries and compare analytical and perturbative methods with full blown nonlinear simulations. Our results include an accurate determination of the merger/scatter transition (consequence of an expanding background) for small mass binaries and a test of the Cosmic Censorship conjecture, for large mass binaries. We observe that, even starting from small separations, black holes in large mass binaries eventually lose causal contact, in agreement with the conjecture.

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**Ondřej Kopáček**

Regular and Chaotic Motion in General Relativity: The Case of a Massive Magnetic Dipole

**Ondřej Kopáček**

Regular and Chaotic Motion in General Relativity: The Case of a Massive Magnetic Dipole

**Abstract: **Circular motion of particles, dust grains and fluids in the vicinity of
compact objects has been investigated as a model for accretion of gaseous
and dusty environment. Here we further discuss, within the framework of
general relativity, figures of equilibrium of matter under the influence
of combined gravitational and large-scale magnetic fields, assuming that
the accreted material acquires a small (but non-vanishing) electric charge
due to interplay of plasma processes and photoionization. In particular,
we employ exact solution describing the massive magnetic dipole and we
identify the regions of stability. We also investigate situations when the
motion exhibits the onset of chaos. In order to characterize the measure
of chaoticness we employ techniques of Poincare surfaces of section and of
recurrence plots.

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**Mariateresa Crosta**

Tracing a relativistic Milky Way within the RAMOD measurement protocol

**Mariateresa Crosta**

Tracing a relativistic Milky Way within the RAMOD measurement protocol

**Abstract: **Advancement in astronomical observations and technical instrumentation implies taking into account the general relativistic effects due the dynamical gravitational fields encountered by the light while propagating from the star to the observer. Therefore, data exploitation for Gaia-like space astrometric mission (ESA, launch 2013) requires a fully relativistic interpretation of the inverse ray-tracing problem, namely the development of a highly accurate astrometric models, named RAMOD, in accordance with the geometrical environment affecting light propagation itself and the precepts of the theory of measurement. This could open a new rendition of the stellar distances and proper motions, or even an alternative detection perspective of many subtle relativistic effects suffered by light while it is propagating and subsequently reordered in the physical measurements.

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**Jiří Svoboda**

On steep radial emissivity in relativistic iron lines

**Jiří Svoboda**

On steep radial emissivity in relativistic iron lines

**Abstract: **X-ray spectroscopy of active galaxies and black hole binaries provides an opportunity to explore the innermost regions of black hole accretion discs. Some of the recent measurements have revealed a very steep radial decrease of the disc reflection emissivity, especially in the central region, suggesting the disc-irradiating corona to be compact and very centrally localised. We will discuss whether the special conditions on the corona properties are indeed required, and/or whether the steep radial emissivity could be an artifact of model assumptions. We will present two different effects which might account for the steep radial emissivities, the angular directionality of the reflected radiation properly calculated in the fully relativistic regime and the radial dependence of the accretion disc ionisation. We will show that these effects may also influence the measurements of the black hole angular momentum.

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**Jiří Horák**

Corotation instability in black-hole accretion disks

**Jiří Horák**

Corotation instability in black-hole accretion disks

**Abstract: **Basic theory of accretion disk oscillations will be reviewed. We will concentrate on the mechanism of the corotation instability. We will present new results for p-modes trapped close to the inner edge of the disk and briefly discuss conditions under which these modes become unstable.

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**Daniele Malafarina**

Equilibrium configurations from gravitational collapse

**Daniele Malafarina**

Equilibrium configurations from gravitational collapse

**Abstract: **
We study how equilibrium configurations can be obtained as the result of gravitational collapse from regular initial conditions within the general theory of relativity. Assuming that the collapsing cloud is composed by a perfect fluid we show that the equilibrium geometries generated by this procedure form a subset of static interior solutions to the Einstein equations. We further show that these static configuration can be either regular or develop a naked singularity at the center, where the presence of a naked singularity is given a precise physical interpretation.
We then study the properties of stable circular orbits around and inside such equilibrium configurations and show that in the case where a naked singularity is present there are key observational differences with respect to the properties of a Schwarzschild black hole with the same mass.
We conclude that if similar objects can form in the universe they could be observationally distinguished from a black hole of the same mass.

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### Conference closing

**Conference closing**in Blue lecture hall