Regularized Conformal Electrodynamics: Novel C-metric in (2+1)
Dimensions
Conformal electrodynamics is a particularly interesting example of power
Maxwell non-linear electrodynamics, designed to possess conformal symmetry in
all dimensions. In this paper, we propose a regularized version of Conformal
electrodynamics, minimally regularizing the field of a point charge at the
origin by breaking the conformal invariance of the theory with a dimensionfull
"Born-Infeld-like" parameter. In four dimensions the new theory reduces to the
recently studied Regularized Maxwell electrodynamics, distinguished by its
"Maxwell-like" solutions for accelerated and slowly rotating black hole
spacetimes. Focusing on three dimensions, we show that the new theory shares
many of the properties of its four-dimensional cousin, including the existence
of the charged C-metric solution (currently unknown in the Maxwell theory).
David Kubiznak
Otakar Svítek
Tayebeh Tahamtan
arxiv:abs
arxiv:pdf
Well-posed non-vacuum solutions in Robinson--Trautman geometry
We study nonlinear matter models compatible with radiative Robinson--Trautman
spacetimes and analyze their stability and well-posedness. The results lead us
to formulate a conjecture relating the (in)stability and well/ill-posedness to
the character of singularity appearing in the solutions. We consider two types
of nonlinear electrodynamics models, namely we provide a radiative ModMax
solution and extend recent results for the RegMax model by considering the
magnetically charged case. In both cases, we investigate linear perturbations
around stationary spherically symmetric solutions to determine the stability
and principal symbol of the system to argue about well-posedness of these
geometries. Additionally, we consider a nonlinear sigma model as a source for
Robinson--Trautman geometry. This leads to stationary solutions with toroidal
(as opposed to spherical) topology thus demanding modification of the analysis.
T. Tahamtan
D. Flores-Alfonso
O. Svitek
doi
Phys. Rev. D 108, 124076 (2023)
arxiv:abs
arxiv:pdf
Solutions and basic properties of regularized Maxwell theory
The regularized Maxwell theory is a recently discovered theory of non-linear
electrodynamics that admits many important gravitating solutions within the
Einstein theory. Namely, it was originally derived as the unique non-linear
electrodynamics (that depends only on the field invariant
$F_{\mu\nu}F^{\mu\nu}$) whose radiative solutions can be found in the
Robinson--Trautman class. At the same time, it is the only electrodynamics of
this type (apart from Maxwell) whose slowly rotating solutions are fully
characterized by the electrostatic potential. In this paper, after discussing
the basic properties of the regularized Maxwell theory, we concentrate on its
spherical electric solutions. These not only provide `the simplest'
regularization of point electric field and its self-energy, but also feature
complex thermodynamic behavior (in both canonical and grandcanonical ensembles)
and admit an unprecedented phase diagram with multiple first-order,
second-order, and zeroth-order phase transitions. Among other notable
solutions, we construct a novel C-metric describing accelerated AdS black holes
in the regularized Maxwell theory. We also present a generalization of the
regularized Maxwell Lagrangian applicable to magnetic solutions, and find the
corresponding spherical, slowly rotating, and weakly NUT charged solutions.
Tomas Hale
David Kubiznak
Ota Svitek
Tayebeh Tahamtan
doi
Phys. Rev. D 107, 124031 (2023)
arxiv:abs
arxiv:pdf
Slowly rotating black holes in nonlinear electrodynamics
We show how (at least in principle) one can construct electrically and
magnetically charged slowly rotating black hole solutions coupled to non-linear
electrodynamics (NLE). Our generalized Lense-Thirring ansatz is, apart from the
static metric function $f$ and the electrostatic potential $\phi$ inherited
from the corresponding spherical solution, characterized by two new functions
$h$ (in the metric) and $\omega$ (in the vector potential) encoding the effect
of rotation. In the linear Maxwell case, the rotating solutions are completely
characterized by static solution, featuring $h=(f-1)/r^2$ and $\omega=1$. We
show that when the first is imposed, the ansatz is inconsistent with any
restricted (see below) NLE but the Maxwell electrodynamics. In particular, this
implies that the (standard) Newman-Janis algorithm cannot be used to generate
rotating solutions for any restricted non-trivial NLE. We present a few
explicit examples of slowly rotating solutions in particular models of NLE, as
well as briefly discuss the NLE charged Taub-NUT spacetimes.
David Kubiznak
Tayebeh Tahamtan
Otakar Svitek
arxiv:abs
arxiv:pdf
Phantom scalar field counterpart to Curzon-Chazy spacetime
We derive and analyze phantom scalar field counterpart to Curzon-Chazy
spacetime. Such solution contains wormhole throat while the region inside the
throat behaves like a one-directional time machine. We describe its conformal
structure and non-scalar singularity hidden inside the wormhole. We examine the
results provided by different definitions of mass of spacetime to understand
their value in the presence of phantom matter. The electromagnetic
generalization of this spacetime is as well briefly considered.
Lukáš Polcar
Otakar Svítek
doi
Classical and Quantum Gravity 39 (2022) 185002
arxiv:abs
arxiv:pdf
Reversing the Null Limit of the Szekeres Metric
The null limits of the Lemaitre-Tolman and Szekeres spacetimes are known to
be the Vaidya and news-free Robinson-Trautman metrics. We generalise this
result to the case of non-zero $\Lambda$, and then ask whether the reverse
process is possible -- is there a systematic procedure to retrieve the
timelike-dust metric from the null-dust case? We present such an algorithm for
re-constructing both the metric and matter tensor components of the
timelike-dust manifold. This undertaking has elucidated the null limit process,
highlighted which quantities approach unity or zero, and necessitated a careful
discussion of how the functional dependencies are managed by the
transformations and substitutions used.
Charles Hellaby
Otakar Svítek
doi
Classical and Quantum Gravity 38, 3, 035004, 2021
arxiv:abs
arxiv:pdf
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 fate of timelike naked singularity with scalar hair
We study the quantum fate of a naked curvature singularity sourced by a
scalar field via several methods and compare the results obtained. The first
method relies on relativistic quantum mechanics on a fixed background employing
the Klein--Gordon and the Dirac equations for a static spacetime. We show that
both the Klein--Gordon and the Dirac particles feel this singularity therefore
this method does not provide its resolution. For comparison, we subsequently
employ methods for quantizing the geometry itself. We selected the canonical
quantization via conditional symmetries and as a last approach we use a maximal
acceleration derivation in the covariant loop quantum gravity. In both of these
approaches the singularity is resolved at the quantum level. We discuss these
conflicting results bearing in mind that quantum particles probe classical
geometry in the first approach while the last two methods quantize the geometry
itself.
O. Svitek
T. Tahamtan
A. Zampeli
doi
Ann. Phys. 418 (2020) 168195
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