Quasilocal horizons in inhomogeneous cosmological models

We investigate quasilocal horizons in inhomogeneous cosmological models, specifically concentrating on the notion of a trapping horizon defined by Hayward as a hypersurface foliated by marginally trapped surfaces. We calculate and analyse these quasilocally defined horizons in two dynamical spacetimes used as inhomogeneous cosmological models with perfect fluid source of non-zero pressure. In the spherically symmetric Lema\^{i}tre spacetime we discover that the horizons (future and past) are both null hypersurfaces provided that the Misner-Sharp mass is constant along the horizons. Under the same assumption we come to the conclusion that the matter on the horizons is of special characte - a perfect fluid with negative pressure. We also find out that they have locally the same geometry as the horizons in the Lema\^{i}tre-Tolman-Bondi spacetime. We then study the Szekeres-Szafron spacetime with no symmetries, particularly its subfamily with $\beta_{,z}\neq 0$, and we find conditions on the horizon existence in a general spacetime as well as in certain special cases.

Eliška Polášková
Otakar Svítek
doi
Class. Quantum Grav. 36 025005 (2019)

arxiv:abs  arxiv:pdf

Quantum probes of timelike naked singularity with scalar hair

We study a curvature singularity resolution via relativistic quantum mechanics on a fixed background based on the Klein--Gordon and the Dirac equations for a static spacetime with a scalar field producing a timelike naked singularity. We show that both the Klein--Gordon and the Dirac particles see this singularity. For comparison with previous method we study the Canonical Quantization via conditional symmetries. Subsequently we check the results by applying a maximal acceleration existence in the Covariant Loop Quantum Gravity described recently and obtain a resolution of singularity. In the process we study radial geodesics and their congruences in the spacetime.

O. Svitek
T. Tahamtan
A. Zampeli
arxiv:abs  arxiv:pdf

Nonsymmetric Dynamical Thin-Shell Wormhole in Robinson--Trautman Class

The thin-shell wormhole created using the Darmois-Israel formalism applied to Robinson-Trautman family of spacetimes is presented. The stress energy tensor created on the throat is interpreted in terms of two dust streams and it is shown that asymptotically this wormhole settles to the Schwarzschild wormhole with a throat located at the horizon position. This behavior shows a nonlinear stability (within the Robinson-Trautman class) of this spherically symmetric wormhole. The gravitational radiation emitted by the Robinson-Trautman wormhole during the transition to spherical symmetry is indistinguishable from that of the corresponding black hole Robinson-Trautman spacetime. Subsequently, we show that the higher-dimensional generalization of Robinson-Trautman geometry offers a possibility of constructing wormholes without the need to violate the energy conditions for matter induced on the throat.

O. Svitek
T. Tahamtan
doi
Eur. Phys. J. C 78 (2018) 167

arxiv:abs  arxiv:pdf

Properties of Robinson--Trautman solution with scalar hair

An explicit Robinson--Trautman solution with minimally coupled free scalar field was derived and analyzed recently. It was shown that this solution possesses a curvature singularity which is initially naked but later enveloped by a horizon. However, this study concentrated on the general branch of the solution where all free constants are nonzero. Interesting special cases arise when some of the parameters are set to zero. In most of these cases the scalar field is still present. One of the cases is a static solution which represents a parametric limit of the Janis--Newman--Winicour scalar field spacetime. Additionally, we provide a calculation of the Bondi mass which clarifies the interpretation of the general solution. Finally, by a complex rotation of a parameter describing the strength of the scalar field we obtain a dynamical wormhole solution.

T. Tahamtan
O. Svitek
doi
Phys. Rev. D 94, 064031 (2016)

arxiv:abs  arxiv:pdf

Robinson--Trautman solution with nonlinear electrodynamics

Explicit Robinson--Trautman solutions with electromagnetic field satisfying nonlinear field equations are derived and analyzed. The solutions are generated from the spherically symmetric ones. In all cases the electromagnetic field singularity is removed while the gravitational one persists. The models resolving curvature singularity were not possible to generalize to Robinson--Trautman geometry indicating that the removal of singularity in associated spherically symmetric case is just a consequence of high symmetry. We show that the solutions are generally of algebraic type II but reduce to type D in spherical symmetry. Asymptotically they tend to the spherically symmetric case as well.

T. Tahamtan
O. Svitek
doi
Eur. Phys. J. C 76 (2016) 335

arxiv:abs  arxiv:pdf

Kundt spacetimes minimally coupled to scalar field

We derive an exact solution belonging to Kundt class of spacetimes both with and without a cosmological constant that are minimally coupled to a free massless scalar field. We show the algebraic type of these solutions and give interpretation of the results. Subsequently, we look for solutions additionally containing an electromagnetic field satisfying nonlinear field equations.

T. Tahamtan
O. Svitek
doi
Eur. Phys. J. C 77 (2017) 384

arxiv:abs  arxiv:pdf

Robinson-Trautman solution with scalar hair

Explicit Robinson-Trautman solution with minimally coupled free scalar field is derived and analyzed. It is shown that this solution contains curvature singularity which is initially naked but later the horizon envelopes it. We use quasilocal horizon definition and prove its existence in later retarded times using sub- and supersolution method combined with growth estimates. We show that the solution is generally of algebraic type II but reduces to type D in spherical symmetry.

T. Tahamtan
O. Svitek
doi
Phys. Rev. D 91: 104032, 2015

arxiv:abs  arxiv:pdf

Averaging in LRS class II spacetimes

We generalize Buchert's averaged equations [Gen. Rel. Grav. 32, 105 (2000); Gen. Rel. Grav. 33, 1381 (2001)] to LRS class II dust model in the sense that all Einstein equations are averaged, not only the trace part. We derive the relevant averaged equations and we investigate backreaction on expansion and shear scalars in an approximate LTB model. Finally we propose a way to close the system of averaged equations.

Petr Kaspar
Otakar Svitek
doi
Gen. Rel. Grav. 47 (2015) 4

arxiv:abs  arxiv:pdf

Modelling Inhomogeneity in Szekeres Spacetime

We study the behaviour of the density contrast in quasi-spherical Szekeres spacetime and derive its analytical behaviour as a function of $t$ and $r$. We set up the inhomogeneity using initial data in the form of one extreme value of the density and the radial profile. We derive conditions for density extremes that are necessary for avoiding the shell crossing singularity and show that in the special case of a trivial curvature function, the conditions are preserved by evolution. We also show that in this special case if the initial inhomogeneity is small, the time evolution does not influence the density contrast, however its magnitude homogeneously decreases.

David Vrba
Otakar Svitek
doi
Gen. Rel. Grav. 46 (2014) 1808

arxiv:abs  arxiv:pdf

Ultrarelativistic boost with scalar field

We present the ultrarelativistic boost of the general global monopole solution which is parametrized by mass and deficit solid angle. The problem is addressed from two different perspectives. In the first one the primary object for performing the boost is the metric tensor while in the second one the energy momentum tensor is used. Since the solution is sourced by a triplet of scalar fields that effectively vanish in the boosting limit we investigate the behavior of a scalar field in a simpler setup. Namely, we perform the boosting study of the spherically symmetric solution with a free scalar field given by Janis, Newman and Winicour. The scalar field is again vanishing in the limit pointing to a broader pattern of scalar field behaviour during an ultrarelativistic boost in highly symmetric situations.

O. Svitek
T. Tahamtan
doi
Gen. Rel. Grav. 48 (2016) 22

arxiv:abs  arxiv:pdf

Averaging in cosmology based on Cartan scalars

We present a new approach for averaging in general relativity and cosmology. After a short review of the theory originally taken from the equivalence problem, we consider two ways how to deal with averaging based on Cartan scalars. We apply the theory for two different LTB models. In the first one, correlation term behaves as a positive cosmological constant, in the second example leading correlation term behaves like spatial curvature. We also show nontriviality of averaging for linearized monochromatic gravitational wave.

Petr Kaspar
Otakar Svitek
doi
Class. Quantum Grav. 31 (2014) 095012

arxiv:abs  arxiv:pdf

Resolution of curvature singularities from quantum mechanical and loop perspective

We analyze the persistence of curvature singularities when analyzed using quantum theory. First, quantum test particles obeying the Klein-Gordon and Chandrasekhar-Dirac equation are used to probe the classical timelike naked singularity. We show that the classical singularity is felt even by our quantum probes. Next, we use loop quantization to resolve singularity hidden beneath the horizon. The singularity is resolved in this case.

T. Tahamtan
O. Svitek
doi
Eur. Phys. J. C 74 (2014) 2987

arxiv:abs  arxiv:pdf

Connection between horizons and algebraic type

We study connections between both event and quasilocal horizons and the algebraic type of the Weyl tensor. The relation regarding spacelike future outer trapping horizon is analysed in four dimensions using double-null foliation.

Otakar Svitek
doi
Springer Proc. in Math. & Stat. 60 (2014) 421

arxiv:abs  arxiv:pdf

Conformal infinity in Robinson-Trautman spacetimes with cosmological constant

In past, the future asymptotic behavior (with respect to initial data on null hypersurface) of Robinson-Trautman spacetime was examined and its past horizon characterized. Therefore, only the investigation of conformal infinity is missing from the picture. We would like to present some initial results concerning conformal infinity when negative cosmological constant is present motivated by the AdS/CFT correspondence.

Otakar Svitek
doi
AIP Conf. Proc. 1458: 531-534, 2012

arxiv:abs  arxiv:pdf

Past horizons in D-dimensional Robinson-Trautman spacetimes

We derive the higher dimensional generalization of Penrose--Tod equation describing past horizon in Robinson--Trautman spacetimes with a cosmological constant and pure radiation. Existence of its solutions in $D>4$ dimensions is proved using tools for nonlinear elliptic partial differential equations. We show that this horizon is naturally a trapping and a dynamical horizon. The findings generalize results from D=4.

Otakar Svitek
doi
Phys.Rev.D84:044027,2011

arxiv:abs  arxiv:pdf

Existence of horizons in Robinson-Trautman spacetimes of arbitrary dimension

We derive the higher dimensional generalization of Penrose-Tod equation describing past horizon in Robinson-Trautman spacetimes with a cosmological constant and pure radiation. Results for D=4 dimensions are summarized. Existence of its solutions in D>4 dimensions is proved using tools for nonlinear elliptic partial differential equations.

Otakar Svitek
doi arxiv:abs  arxiv:pdf

Features of gravitational waves in higher dimensions

There are several fundamental differences between four-dimensional and higher-dimensional gravitational waves, namely in the so called braneworld set-up. One of them is their asymptotic behavior within the Cauchy problem. This study is connected with the so called Hadamard problem, which aims at the question of Huygens principle validity. We investigate the effect of braneworld scenarios on the character of propagation of gravitational waves on FRW background.

Otakar Svitek
doi
J.Phys.Conf.Ser.229:012070,2010

arxiv:abs  arxiv:pdf

Past horizons in Robinson-Trautman spacetimes with a cosmological constant

We study past horizons in the class of type II Robinson-Trautman vacuum spacetimes with a cosmological constant. These exact radiative solutions of Einstein's equations exist in the future of any sufficiently smooth initial data, and they approach the corresponding spherically symmetric Schwarzschild-(anti-)de Sitter metric. By analytic methods we investigate the existence, uniqueness, location and character of the past horizons in these spacetimes. In particular, we generalize the Penrose-Tod equation for marginally trapped surfaces, which form such white-hole horizons, to the case of a nonvanishing cosmological constant, we analyze behavior of its solutions and visualize their evolutions. We also prove that these horizons are explicit examples of an outer trapping horizon and a dynamical horizon, so that they are spacelike past outer horizons.

Jiri Podolsky
Otakar Svitek
doi
Phys.Rev.D80:124042,2009

arxiv:abs  arxiv:pdf

Apparent horizons in D-dimensional Robinson-Trautman spacetime

We derive the higher dimensional generalization of Penrose-Tod equation describing apparent horizons in Robinson-Trautman spacetimes. New results concerning the existence and uniqueness of its solutions in four dimensions are proven. Namely, previous results of Tod are generalized to nonvanishing cosmological constant.

Otakar Svitek
doi
AIP Conf.Proc.1122:404-407,2009

arxiv:abs  arxiv:pdf

The damping of gravitational waves in dust

We examine a simple model of interaction of gravitational waves with matter (primarily represented by dust). The aim is to investigate a possible damping effect on the intensity of gravitational wave when passing through media. This might be important for gravitational wave astronomy when the sources are obscured by dust or molecular clouds.

Otakar Svitek
doi
Phys.Scripta 79:025003,2009

arxiv:abs  arxiv:pdf

Evolution of high-frequency gravitational waves in some cosmological models

We investigate Isaacson's high-frequency gravitational waves which propagate in some relevant cosmological models, in particular the FRW spacetimes. Their time evolution in Fourier space is explicitly obtained for various metric forms of (anti--)de Sitter universe. Behaviour of high-frequency waves in the anisotropic Kasner spacetime is also described.

Otakar Svitek
Jiri Podolsky
doi
Czech.J.Phys. 56 (2006) 1367-1380

arxiv:abs  arxiv:pdf

Radiative spacetimes approaching the Vaidya metric

We analyze a class of exact type II solutions of the Robinson-Trautman family which contain pure radiation and (possibly) a cosmological constant. It is shown that these spacetimes exist for any sufficiently smooth initial data, and that they approach the spherically symmetric Vaidya-(anti-)de Sitter metric. We also investigate extensions of the metric, and we demonstrate that their order of smoothness is in general only finite. Some applications of the results are outlined.

Jiri Podolsky
Otakar Svitek
doi
Phys.Rev. D71 (2005) 124001

arxiv:abs  arxiv:pdf

The Efroimsky formalism adapted to high-frequency perturbations

The Efroimsky perturbation scheme for consistent treatment of gravitational waves and their influence on the background is summarized and compared with classical Isaacson's high-frequency approach. We demonstrate that the Efroimsky method in its present form is not compatible with the Isaacson limit of high-frequency gravitational waves, and we propose its natural generalization to resolve this drawback.

Otakar Svitek
Jiri Podolsky
doi
Class.Quant.Grav. 21 (2004) 3579-3586

arxiv:abs  arxiv:pdf

Some high-frequency gravitational waves related to exact radiative spacetimes

A formalism is introduced which may describe both standard linearized waves and gravitational waves in Isaacson's high-frequency limit. After emphasizing main differences between the two approximation techniques we generalize the Isaacson method to non-vacuum spacetimes. Then we present three large explicit classes of solutions for high-frequency gravitational waves in particular backgrounds. These involve non-expanding (plane, spherical or hyperboloidal), cylindrical, and expanding (spherical) waves propagating in various universes which may contain a cosmological constant and electromagnetic field. Relations of high-frequency gravitational perturbations of these types to corresponding exact radiative spacetimes are described.

Jiri Podolsky
Otakar Svitek
doi
Gen.Rel.Grav. 36 (2004) 387-401

arxiv:abs  arxiv:pdf