Extended EPS structure for $f(R, R_{\mu\nu} R^{\mu\nu})$ gravity theories in Palatini formalism

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Written by Azam Izadi

An axiomatic understanding of the foundations of any reasonable theory of the space--time and gravity was represented by Ehlers, Pirani and Schild (EPS), which leaves a special effect on the observational protocols in such a way that not all standard protocols can be trivially extended to a general extended theory of gravity. In addition, for a generic Palatini modified gravity theory, in a frame with the locally vanishing affine connection, the degeneracy of known aspects of the speed of light is breaking in the presence of matter and hence results in breaking the equivalence principle. Furthermore, some aspects of it may become variable in the aforementioned local frame. Following these results, we consider a general $f(R, R_{\mu\nu} R^{\mu\nu})$ gravity theory in the Palatini formalism. We study the equivalence principle and different manifestations of the speed of light in this general theory. In addition, the EPS structure on the space-time is extended for this generic Palatini gravity theories. Finally, we compare the results with standard GR.

Dynamics of an Anisotropic Universe in f(R,T) Theory

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Written by Bivudutta Mishra

Dynamics of an anisotropic universe is studied in $f(R,T)$ gravity using a rescaled functional $f(R,T)$.
Three models have been constructed assuming a power law expansion of the universe. Physical features of
the models are discussed. The model parameters are constrained from a dimensional analysis. It is found
from the work that, the $BVI_h$ model in the modified gravity can favour quintessence and phantom phase.

Rotating Excited Boson Stars

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Written by Lucas Gardai Collodel

We investigate axially symmetric, rotating boson stars which are radially excited. These objects exist only for a limited range of the field's frequency. Given different coupling strengths with gravity we determine its domain of existence, as well as the frequency dependence behaviour of the star's parameters, which is then compared with the non-excited case. The circular orbit's tangential velocity of test particles around such objects is also analysed in order to determine if their existence offers a good alternative for dark matter at the galactic scale.

Lower bounds of collisional energy near Kerr black holes

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Written by Mieszko Rutkowski

During my talk, I will discuss collisions of test particles in Kerr spacetime. After reviewing studies on upper bounds of collisional energy, I will examine lower bounds of collisional energy between orbiting and infalling particles.

Initial data for the Einstein equations with positive cosmological constant

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Written by Jerzy Knopik

In this talk I report on work in progress on Bowen-York type initial data with positive cosmological constant.

Dain's invariant on non-time symmetric initial data sets

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Written by Jarrod Williams

The question of stability of certain special solutions is one of the central concerns of mathematical Relativity.
In such problems, it would be useful to have a way of quantifying, in a coordinate-invariant manner, the extent to which a given initial data set deviates from a stationary regime. One approach, proposed by S. Dain,
is based on the notion of an approximate Killing vector, constructed as a solution to a fourth-order elliptic system arising from the Killing Initial Data equations. The approximate Killing vector, which was shown to exist for time symmetric initial data, may then be used to define an invariant which characterises stationarity. In this talk I will present recent work extending Dain's result to the case of non-time symmetric asymptotically Euclidean initial data, concluding with a discussion of some applications.

Killing spinor data in the characteristic problem

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Written by Michael Cole

The existence of a Killing spinor can be used to show that a spacetime is a member of the Kerr family, so finding ways of guaranteeing this in terms of initial or boundary data can be of interest. We show that the existence of a Killing spinor in the domain of dependence of a pair of intersecting, non-expanding null hypersurfaces can be characterised as data only on the bifurcation sphere, where these hypersurfaces intersect. This can be used to obtain a uniqueness result for stationary vacuum black holes spacetimes in the domain of dependence.

The relativistic geoid: redshift and acceleration potential

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Written by Dennis Philipp

We construct a relativistic geoid based on a time-independent redshift potential, which foliates the spacetime into isochronometric surfaces. This relativistic potential coincides with the acceleration potential for isometric congruences. We show that the a- and u- geoid, defined in a post-Newtonian framework, coincide also in a more general setup. Known Newtonian and post-Newtonian results are recovered in the respective limits. Our approach offers a relativistic definition of the Earth's geoid as well as a description of the Earth itself (or observers on its surface) in terms of an isometric congruence. Being fully relativistic, this notion of a geoid can also be applied to other compact objects such as neutron stars.

By definition, this relativistic geoid can be determined by a congruence of Killing observers equipped with standard clocks by comparing their frequencies as well as by measuring accelerations of objects that follow the congruence. The redshift potential gives the correct result also for frequency comparison through optical fiber links as long as the fiber is at rest w.r.t. the congruence.

We give explicit expressions for the relativistic geoid in the Kerr spacetime and the Weyl class of spacetimes. To investigate the influence of higher order mass multipole moments we compare the results for the Schwarzschild case to those obtained for the Erez-Rosen and q-metric spacetimes.

Second-order relativistic fluids break conservation laws

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Written by Vojtěch Witzany

Higher-order fluids are fluids which have higher-order gradient terms in their stress-energy tensor. It is well established that at least second-order fluids are needed for a causal relativistic theory of dissipation. Furthermore, the question of even higher-order fluids arose recently in the context of the AdS/CFT correspondence where the higher-order fluid dynamics emerge as an effective-field description of the conformal field on the boundary. In this talk, we will deliver a simple theoretical argument which suggests that, starting with order 2, effective higher-order fluid descriptions must generically break conservation of the stress-energy tensor and the conservation of Noether currents.

Analyzing black hole shadows on Kerr spacetimes

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Written by Marius Oancea

The shadow of a black hole can be defined as the innermost trajectory on which light from a background source passing a black hole can reach the observer. We prove that for any observer in the domain of outer communication of any subextremal Kerr spacetime the shadow of the black hole is represented by a smooth curve on the celestial sphere of that observer. Furthermore, we present numerical evidence that the radial degeneracy of the black hole shadow is broken in Kerr spacetimes for observers away from the symmetry axis. These results are available at https://arxiv.org/abs/1611.06927.

Joint work with Claudio Paganini and Blazej Ruba.

Symmetries of linearized Einstein equations on Kerr spacetime

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Written by Steffen Aksteiner

Motivated by the black hole stability problem, we discuss the structure of linear test fields on Kerr spacetime. The dynamics of the linearized gravitational field on a Kerr background is governed by certain curvature components solving the Teukolsky master equations (TME) and Teukolsky-Starobinski identities (TSI). I will show that the TME and TSI operators are self-adjoint in an appropriate sense. Combined with a result due to Wald from 1978, this leads to symmetry operators of the linearized Einstein equations of order four and six, respectively. The results are derived using spinors and advanced symbolic computer algebra tools for xAct.

Dragging and anti-dragging effects in rotating disk systems

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Written by Michal Piróg

I will discuss hydrodynamical post-Newtonian models of self-gravitating stationary black-hole-disk systems. The recently discovered new class of rotation laws, which contain the general-relativistic extension of Newtonian rotation law, was applied to obtain the solution. There is strong numerical evidence that various types of dragging (anti-dragging) effects are positively correlated with the normalized angular momentum. I am going to present the numerical results for many different numerical models which show the relation between the above-mentioned effects and such parameters of the system like total mass and asymptotic angular momentum.

Degrees of freedom of weak gravitational field on a spherically symmetric background

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Written by Piotr Waluk

We present a way of reducing ADM data for the Cauchy problem for linearized gravity on a Kottler background (i.e. general spherically symmetric vacuum solution with cosmological constant)  to a set of four gauge-invariant unconstrained scalar functions on the initial surface, containing whole information about the perturbation. This is a generalization of earlier results by J. Jezierski and J. Kijowski for Minkowski and Schwarzschild backgrounds.

The Einstein-Λ flow on product manifolds

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Written by Klaus Kröncke

We consider the vacuum Einstein flow with a positive cosmological constant on spatial manifolds of product form. In spatial dimension at least four we show the existence of continuous families of recollapsing models whenever at least one of the factors or admits a Riemannian Einstein metric with positive Einstein constant. We moreover show that these families belong to larger continuous families with models that have two complete time directions, i.e. do not recollapse. Complementarily, we show that whenever no factor has positive curvature, then any model in the product class expands in one time direction and collapses in the other. In particular, positive curvature of one factor is a necessary criterion for recollapse within this class. Finally, we relate our results to the instability of the Nariai solution in three spatial dimensions and point out why a similar construction of recollapsing models in that dimension fails. The present results imply that there exist different classes of initial data which exhibit fundamentally different types of long-time behavior under the Einstein flow whenever the spatial dimension is strictly larger than three. Moreover, this behavior is related to the spatial topology through the existence of Riemannian Einstein metrics of positive curvature.

(This is joint work with David Fajman)

Accretion onto almost Kerr-de Sitter black holes

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Written by Filip Ficek

The Reissner–Nordström solution resembles certain features characteristic for the Kerr solution - specifically they share the causal and horizon structures. This fact lets us suspect, that considering an accretion onto spherically symmetric charged black holes may give us an insight into an accretion onto less symmetric rotating black holes. During my speech I want to focus on the Bondi-type accretion in the Reissner-Nordström-(anti-)de Sitter spacetime. I will consider an accretion of the isothermal and polytropic test fluids, and show that in some specific cases one can obtain the analytic solutions. I will also give some remarks about the existing homoclinic solutions. Finally I will show the dependence between positions of the horizons and the photon gas sonic points.

A numerical solver for Einstein's constraint equations as a parabolic-hyperbolic system

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Written by Christian Schell

Einstein's field equations contain a system of constraints.
Very often they are considered as elliptic equations (with benefits but also drawbacks).
Only recently István Rácz initiated systematic studies of the constraints as an evolutionary system.
In this talk I will review some of the basics and present a numerical verification of the previously obtained analytical results.
I consider linear perturbations of Minkowski spacetime and the full nonlinear equations in axisymmetry.
This is part of a joint project with Oliver Rinne to model Einstein's axisymmetric vacuum equations in a constrained evolution scheme using spherical polar coordinates with a regular center.

Polish spaces of causal curves

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Written by Tomasz Miller

I will present a new approach to the topologization of the set of (possibly not all) causal curves on a stably causal spacetime. It relies on parametrizing the curves "in accordance" with a chosen time function. Thus obtained spaces turn out to possess certain nice topological and measure-theoretic properties - they are Polish.

In the second part of my talk, drawing from our earlier work on the causality between probability measures, I will discuss how the said Polish spaces of causal curves can be applied to the description of the causal time-evolution of spatially distributed physical quantities (like the charge or energy density) in globally hyperbolic spacetimes.

The talk will be mainly based on the preprint https://arxiv.org/abs/1609.09488

Non-singular stationary spacetimes with negative cosmological constant and various matter fields

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Written by Paul Klinger

We present infinite-dimensional families of non-singular stationary space times, solutions of the Yang-Mills-Higgs-Einstein-Maxwell-Chern-Simons-dilaton-scalar field equations. The solutions are constructed using an implicit function argument around "non-degenerate" vacuum solutions (defined by requiring an operator associated with the linearisation of the equations to be an isomorphism). As Anti-de Sitter space is one example of such a solution, the constructed families include an infinite-dimensional family of solutions with the usual AdS conformal structure at conformal infinity.

This is joint work with Piotr Chrusciel and Erwann Delay.

Zero rest-mass fields and the Newman-Penrose constants on flat space

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Written by Edgar Gasperin-Garcia

Zero rest-mass fields of spin 1 (the electromagnetic field) and spin 2 propagating on flat space and their corresponding Newman-Penrose (NP) constants are studied near spatial infinity. The aim of this analysis is to clarify the correspondence between data for these fields on a spacelike hypersurface and the value of their corresponding NP constants at future and past null infinity. To do so, the framework of the cylinder at spatial infinity is employed to show that, expanding the initial data in terms spherical harmonics and powers of the geodesic spatial distance ρ to spatial infinity, the NP constants correspond to the data for the highest possible spherical harmonic at fixed order in ρ. In addition, it is shown that the NP constants at future and past null infinity, for both the Maxwell and spin-2 case, are related to each other as they arise from the same terms in the initial data. Moreover, it is shown that this observation is true for generic data (not necessarily time-symmetric). This identification is a consequence of both the evolution and constraint equations.

Examples of toroidal trapped surfaces

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Written by Patryk Mach

This is a joint work with Janusz Karkowski, Edward Malec, Niall O Murchadha and Naqing Xie on trapped toroidal surfaces. We construct (analytically) an infinite number of trapped toroids in spherically symmetric Cauchy hypersurfaces of the Einstein equations. We focus on initial data which represent "constant density stars" momentarily at rest. There exists an infinite number of constant mean curvature tori, but we also deal with more general configurations. The marginally trapped toroids have been found analytically and numerically; they are unstable. The topologically toroidal trapped surfaces appear in a finite region surrounded by the Schwarzschild horizon. The corresponding paper is posted on arXiv as arXiv:1701.02861

Singularity theorems in low regularity

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Written by Melanie Graf

Many classical results of general relativity require the spacetime metric to be at least twice continuously differentiable which is somewhat unsatisfactory from a physical point of view. In recent years there has been increased interest in low regularity spacetimes leading to proofs of both the Hawking and the Penrose singularity theorem for C^1,1-metrics (i.e., continuously differentiable metrics with Lipschitz continuous first derivatives). These proofs are based on new approximation techniques due to Chruściel and Grant which respect the causal structure. However, the more general singularity theorem of Hawking and Penrose has yet to be proven in this regularity.
       In my talk I would like to give a brief overview about the aforementioned proofs and discuss the various difficulties that arise when trying to prove the Hawking and Penrose singularity theorem in a similar fashion as well as our recent progress in overcoming (some of) those difficulties.

The gravitomagnetic clock effect and pulsar timing

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Written by Eva Hackmann

In General Relativity the rotation of a gravitating object influences the spacetime in its vicinity, which is called frame dragging or gravitomagnetism. Related to this is the Lense-Thirring effect due to spin-orbit coupling, measured by the LAGEOS/LARES missions, and the Schiff effect due to spin-spin coupling, measured by the Gravity Probe B mission. Here we will discuss a frame dragging effect on clocks, the gravitomagnetic clock effect first analysed by Cohen and Mashhoon (Physics Letters A 181 (1993) 353) for the case of two clocks on counter-revolving equatorial circular orbits. We show how this effect can be defined for two clocks on arbitrary geodesic orbits in Kerr spacetime and discuss its magnitude for two pulsars orbiting Sagittarius A*.

A continuous Riemann-Hilbert problem for colliding plane gravitational waves

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Written by Stefan Palenta

I will present the foundations of a new solution technique for the characteristic initial value problem (IVP) of colliding plane gravitational waves. The corresponding spacetime features a two-dimensional orthogonally transitive group of isometries essentially reducing the Einstein equations to the hyperbolic Ernst equation. Its solution can be constructed via the so-called inverse scattering method using a linear system of partial differential equations and a Riemann-Hilbert problem (RHP). Inevitable nonanalytic behaviour of the initial data at the wavefronts leads to singularities in the integral equation determining the RHP solution. Therefore, a transformation to a continuous RHP with a solution given in terms of non-singular integral equations is introduced. Ambiguities in this procedure lead to the construction of a family of spacetimes containing the solution to the IVP. Hence the described technique may also serve as an interesting solution generating method.

Near-Horizon Extreme Kerr Magnetospheres

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Written by Roberto Oliveri

Black holes surrounded by an accreting plasma admit a very rich dynamics. Under the assumption of vanishing Lorentz force density and negligible matter backreaction, the dynamics of the black hole magnetosphere is governed by Force-Free Electrodynamics (FFE) in the fixed background geometry. The FFE equations are highly nonlinear and typically can only be solved numerically. In this talk, I consider FFE in the Near-Horizon geometry of an Extreme Kerr black hole (NHEK). First, I show how several classes of exact analytical solutions can be found thanks to the enhanced isometry group of NHEK spacetime. Second, I characterize those potentially physical solutions with finite energy and angular momentum fluxes with respect to the asymptotically flat observer.

Alternative to supersymmetry: conservative extensions of the spacetime covariance group

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Written by Andras Laszlo

In this talk we show that there exists a mathematical alternative to the concept of local supersymmetry (SUSY), in general relativistic field theories. Since, up to now, there is no experimental indication to the existence of SUSY in Nature, this can be a possible way out for creating Lagrangians with unified gauge-and-spacetime covariance group, without SUSY. Our alternatives are the conservative extensions of the spacetime covariance group, meaning that --in contrast to SUSY-- all the field transformations complementing the spacetime covariance group are inner. That is, they act pointwise, similarly as the gauge transformations act in a conventional local gauge theory.
(based on: IJMPA31(2016)1645041 and arXiv:1512.03328 -- in review at J.Phys.A)

Symmetry inheritance and no-hair theorems

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Written by Ivica Smolić

We say that a matter or a gauge field inherits a spacetime symmetry, generated by a Killing vector field, if it is necessarily invariant under the action of that Killing vector field. Symmetry inheritance is not only used as a convenient assumption in a choice of the ansatz, but is also an important ingredient of the various gravitational uniqueness theorems. Its breaking may point to some novel, potentially interesting physical phenomena, such as the recently discovered rotating black hole solutions with the complex scalar hair.

In this talk I shall present an overview of the recent novel results about the symmetry inheritance of the real and the complex scalar fields [1,3], as well as the symmetry inheritance of the electromagnetic field in (1+2)-dimensional spacetimes [2]. Also, I will discuss the ramifications of these theorems on the classification of the black hole hair, and present a survey of various open problems.

[1] I. Smolić: Symmetry Inheritance of Scalar Fields, Class. Quantum Grav. 32 (2015) 145010 [arXiv: 1501.04967]

[2] M. Cvitan, P. Dominis Prester and I. Smolić: Does three dimensional electromagnetic field inherit the spacetime symmetries?, Class. Quantum Grav. 33 (2016) 077001 [arXiv: 1508.03343]

[3] I. Smolić: Constraints on the symmetry noninheriting scalar black hole hair, Phys. Rev. D 95 (2017) 024016 [arXiv: 1609.04013]

Can we use gravity to produce ultra-high energy cosmic rays and neutrinos ?

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Written by Mandar Patil

Origin of ultra-high energy cosmic rays and neutrinos remains an enigma. All proposed mechanisms use electromagnetic interaction to accelerate changed particles. We propose for the first time, a mechanism that exclusively makes use of Gravity, rather than the electromagnetic forces. We show that it is possible to generate ultra-high energy particles in the overspinning Kerr geometry transcending Kerr bound by a small amount. We compute spectrum of the ultra-high energy particles and argue that its shape could serve as a powerful probe of particle physics. By solving the constraint equations in numerical relativity we show that the overspinning Kerr geometry could occur in the gravitational collapse scenario. It was also argued by Horava that overspinning spacetimes could be realized in the context of string theory. We also speculate on the other spacetime geometries where a similar acceleration mechanism could be at work.

Based on  Phys. Rev. D 93, 104015 (2016),  Phys. Rev. D 90, 124079 (2014).

Hidden symmetries and decay for the Vlasov equation on the Kerr spacetime

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Written by Jeremie Joudioux

We prove the existence of a bounded energy and integrated energy decay for solutions of the massless Vlasov equation in the exterior of a very slowly rotating Kerr spacetime. This combines methods previously developed to prove similar results for the wave equation on the exterior of a very slowly rotating Kerr spacetime with recent work applying the vector-field method to the relativistic Vlasov equation. This work is a collaboration with P. Blue and L. Andersson.

Axisymmetric MP solutions

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Written by Jiří Ryzner

We first introduce two distinct solutions of Einstein-Maxwell(-dilaton) equations. In addition to being axially symmetric and static, the solutions are reflection symmetric with respect to some special planes and exhibit a discrete translational symmetry along the axis. We discuss their properties and compare them to a Majumdar-Papapetrou solution involving two black holes, which has the same continuous symmetries.

Higher order perturbations of Anti-de Sitter space and time-periodic solutions of vacuum Einstein equations

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Written by Andrzej Rostworowski

Motivated by the problem of stability of Anti-de Sitter (AdS) spacetime, we will discuss nonlinear grav-
itational perturbations of maximally symmetric solutions of vacuum Einstein equations in general
and the case of AdS in particular. We will present the evidence that, similarly to the self-gravitating
scalar field at spherical symmetry, the negative cosmological constant allows for the existence of
globally regular, asymptotically AdS, time-periodic solutions of vacuum Einstein equations that bi-
furcate from linear eigenfrequencies of AdS. Interestingly, preliminary results indicate that the
number of time-periodic solutions bifurcating from a given eigenfrequency equals the multiplicity of
this eigenfrequency.