arXiv subjects

Jiri Podolsky

Publications and source records attributed to Jiri Podolsky.

At least 73 records · Page 4Linked to original sources

arXiv2010

Refraction of geodesics by impulsive spherical gravitational waves in constant-curvature spacetimes with a cosmological constant

We investigate motion of test particles in exact spacetimes with an expanding impulsive gravitational wave which propagates in Minkowski, de Sitter or anti-de Sitter universe. Using the continuous form of these metrics we derive explicit junction conditions and simple refraction formulae for null, timelike and spacelike geodesics crossing a general impulse of this type. In particular, we present a detailed geometrical description of the motion of test particles in a special class of axially symmetric spacetimes in which the impulse is generated by a snapped cosmic string.

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arXiv2009

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.

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arXiv2009

Gyratons on direct-product spacetimes

We present and analyze exact gyraton and nonexpanding gravitational wave solutions of algebraic type II on backgrounds which are a direct-product of two 2-spaces of constant curvature, or more general type D spacetimes. This family of electro-vacuum background spacetimes contains the Nariai, anti-Nariai and Plebanski-Hacyan universes, conformally flat Bertotti-Robinson and Minkowski spaces. The gyraton solutions are given in a simple Kundt metric form. They belong to the recently discussed class of spacetimes with constant scalar invariants (CSI) of the curvature tensor. We show that the Einstein equations reduce to a set of linear equations on the transverse 2-space which can be explicitly solved using the Green functions.

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arXiv2009

Radiation generated by accelerating and rotating charged black holes in (anti-)de Sitter space

Asymptotic behaviour of gravitational and electromagnetic fields of exact type D solutions from the large Plebanski-Demianski family of black hole spacetimes is analyzed. The amplitude and directional structure of radiation is evaluated in cases when the cosmological constant is non-vanishing, so that the conformal infinities have either de Sitter-like or anti-de Sitter-like character. In particular, explicit relations between the parameters that characterize the sources (that is their mass, electric and magnetic charges, NUT parameter, rotational parameter, and acceleration) and properties of the radiation generated by them are presented. The results further elucidate the physical interpretation of these solutions and may help to understand radiative characteristics of more general spacetimes than those that are asymptotically flat.

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arXiv2009

On conformally flat and type N pure radiation metrics

We study pure radiation spacetimes of algebraic types O and N with a possible cosmological constant. In particular, we present explicit transformations which put these metrics, that were recently re-derived by Edgar, Vickers and Machado Ramos, into a general Ozsvath-Robinson-Rozga form. By putting all such metrics into the unified coordinate system we confirm that their derivation based on the GIF formalism is correct. We identify only few trivial differences.

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arXiv2008

General Kundt spacetimes in higher dimensions

We investigate a general metric of the Kundt class of spacetimes in higher dimensions. Geometrically, it admits a non-twisting, non-shearing and non-expanding geodesic null congruence. We calculate all components of the curvature and Ricci tensors, without assuming any specific matter content, and discuss algebraic types and main geometric constraints imposed by general Einstein's field equations. We explicitly derive Einstein-Maxwell equations, including an arbitrary cosmological constant, in the case of vacuum or possibly an aligned electromagnetic field. Finally, we introduce canonical subclasses of the Kundt family and we identify the most important special cases, namely generalised pp-waves, VSI or CSI spacetimes, and gyratons.

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arXiv2008

Photon rockets in (anti-)de Sitter universe

A class of exact solutions of Einstein's equations is presented which describes accelerating photon rockets in de Sitter and anti-de Sitter universe. These are particular members of the Robinson-Trautman family of axially symmetric spacetimes with pure radiation. In particular, generalizations of (type D) Kinnersley's rockets and (type II) Bonnor's rockets to the case of a non-vanishing cosmological constant are given. Some of the main physical properties of these solutions are investigated, and their relation to the C-metric solution which describes uniformly accelerated black holes is also given.

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arXiv2007

Robinson-Trautman spacetimes with an electromagnetic field in higher dimensions

We investigate higher dimensional Robinson-Trautman spacetimes with an electromagnetic field aligned with the hypersurface orthogonal, non-shearing, expanding geodesic null congruence. After integrating the system of Einstein-Maxwell equations with an arbitrary cosmological constant, we present the complete family of solutions. In odd spacetime dimensions they represent (generalized) Reissner-Nordstrom-de Sitter black holes. The event horizon (more generically, the transverse space) may be any Einstein space, and the full metric is specified by three independent parameters related to mass, electric charge and cosmological constant. These solutions also exhaust the class of Robinson-Trautman spacetimes with an aligned Maxwell-Chern-Simons field (the CS term must vanish because of the alignment assumption and of the Einstein equations). In even dimensions an additional magnetic "monopole-like" parameter is also allowed provided now the transverse space is an (almost-)Kahler Einstein manifold. The Weyl tensor of all such solutions is of algebraic type D. We also consider the possible inclusion of aligned pure radiation.

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arXiv2007

Chaotic motion in Kundt spacetimes

We demonstrate that geodesics in exact vacuum Kundt gravitational waves may exhibit a highly complicated behaviour. In fact, as in the previously studied case of non-homogeneous pp-waves, for specific choices of the structural function the motion appears to be genuinely chaotic. This fact is demonstrated by the fractal method.

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arXiv2006

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.

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arXiv2006

Robinson-Trautman spacetimes in higher dimensions

As an extension of the Robinson-Trautman solutions of D=4 general relativity, we investigate higher dimensional spacetimes which admit a hypersurface orthogonal, non-shearing and expanding geodesic null congruence. Einstein's field equations with an arbitrary cosmological constant and possibly an aligned pure radiation are fully integrated, so that the complete family is presented in closed explicit form. As a distinctive feature of higher dimensions, the transverse spatial part of the general line element must be a Riemannian Einstein space, but it is otherwise arbitrary. On the other hand, the remaining part of the metric is - perhaps surprisingly - not so rich as in the standard D=4 case, and the corresponding Weyl tensor is necessarily of algebraic type D. While the general family contains (generalized) static Schwarzschild-Kottler-Tangherlini black holes and extensions of the Vaidya metric, there is no analogue of important solutions such as the C-metric.

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arXiv2006

Asymptotic structure of radiation in higher dimensions

We characterize a general gravitational field near conformal infinity (null, spacelike, or timelike) in spacetimes of any dimension. This is based on an explicit evaluation of the dependence of the radiative component of the Weyl tensor on the null direction from which infinity is approached. The behaviour similar to peeling property is recovered, and it is shown that the directional structure of radiation has a universal character that is determined by the algebraic type of the spacetime. This is a natural generalization of analogous results obtained previously in the four-dimensional case.

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arXiv2005

Ultrarelativistic boost of spinning black rings

We study the D=5 Emparan-Reall spinning black ring under an ultrarelativistic boost along an arbitrary direction. We analytically determine the resulting shock pp-wave, in particular for boosts along axes orthogonal and parallel to the plane of rotation. The solution becomes physically more interesting and simpler if one enforces equilibrium between the forces on the ring. We also comment on the ultrarelativistic limit of recently found supersymmetric black rings with two independent angular momenta. Essential distinct features with respect to the boosted Myers-Perry black holes are pointed out.

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arXiv2005

Ultrarelativistic boost of the black ring

We investigate the ultrarelativistic boost of the five-dimensional Emparan-Reall non-rotating black ring. Following the classical method of Aichelburg and Sexl, we determine the gravitational field generated by a black ring moving ``with the speed of light'' in an arbitrary direction. In particular, we study in detail two different boosts along axes orthogonal and parallel to the plane of the ring circle, respectively. In both cases, after the limit one obtains a five-dimensional impulsive pp-wave propagating in Minkowski spacetime. The curvature singularity of the original static spacetime becomes a singular source within the wave front, in the shape of a ring or a rod according to the direction of the boost. In the case of an orthogonal boost, the wave front contains also a remnant of the original disk-shaped membrane as a component of the Ricci tensor (which is everywhere else vanishing). We also analyze the asymptotic properties of the boosted black ring at large spatial distances from the singularity, and its behaviour near the sources. In the limit when the singularity shrinks to a point, one recovers the well known five-dimensional analogue of the Aichelburg-Sexl ``monopole'' solution.

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arXiv2005

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.

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arXiv2005

Asymptotic directional structure of radiative fields in spacetimes with a cosmological constant

We analyze the directional properties of general gravitational, electromagnetic, and spin-s fields near conformal infinity I. The fields are evaluated in normalized tetrads which are parallelly propagated along null geodesics which approach a point P of I. The standard peeling-off property is recovered and its meaning is discussed and refined. When the (local) character of the conformal infinity is null, such as in asymptotically flat spacetimes, the dominant term which is identified with radiation is unique. However, for spacetimes with a non-vanishing cosmological constant the conformal infinity is spacelike (for Lambda>0) or timelike (for Lambda<0), and the radiative component of each field depends substantially on the null direction along which P is approached. The directional dependence of asymptotic fields near such de Sitter-like or anti-de Sitter-like I is explicitly found and described. We demonstrate that the corresponding directional structure of radiation has a universal character that is determined by the algebraic (Petrov) type of the field. In particular, when Lambda>0 the radiation vanishes only along directions which are opposite to principal null directions. For Lambda<0 the directional dependence is more complicated because it is necessary to distinguish outgoing and ingoing radiation. Near such anti-de Sitter-like conformal infinity the corresponding directional structures differ, depending not only on the number and degeneracy of the principal null directions at P but also on their specific orientation with respect to I. The directional structure of radiation near (anti-)de Sitter-like infinities supplements the standard peeling-off property of spin-s fields. This offers a better understanding of the asymptotic behaviour of the fields near conformal infinity.

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arXiv2005

Asymptotic directional structure of radiation for fields of algebraic type D

The directional behavior of dominant components of algebraically special spin-s fields near a spacelike, timelike or null conformal infinity is studied. By extending our previous general investigations we concentrate on fields which admit a pair of equivalent algebraically special null directions, such as the Petrov type D gravitational fields or algebraically general electromagnetic fields. We introduce and discuss a canonical choice of the reference tetrad near infinity in all possible situations, and we present the corresponding asymptotic directional structures using the most natural parametrizations.

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arXiv2004

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.

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