### 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