arXiv subjects

J. Podolsky

Publications and source records attributed to J. Podolsky.

35 records · Page 2Linked to original sources

arXiv2000

The collision and snapping of cosmic strings generating spherical impulsive gravitational waves

The Penrose method for constructing spherical impulsive gravitational waves is investigated in detail, including alternative spatial sections and an arbitrary cosmological constant. The resulting waves include those that are generated by a snapping cosmic string. The method is used to construct an explicit exact solution of Einstein's equations describing the collision of two nonaligned cosmic strings in a Minkowski background which snap at their point of collision.

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arXiv1999

The structure of the extreme Schwarzschild-de Sitter space-time

The extreme Schwarzschild-de Sitter space-time is a spherically symmetric solution of Einstein's equations with a cosmological constant Lambda and mass parameter m>0 which is characterized by the condition that 9 Lambda m^2=1. The global structure of this space-time is here analyzed in detail. Conformal and embedding diagrams are constructed, and synchronous coordinates which are suitable for a discussion of the cosmic no-hair conjecture are presented. The permitted geodesic motions are also analyzed. By a careful investigation of the geodesics and the equations of geodesic deviation, it is shown that specific families of observers escape from falling into the singularity and approach nonsingular asymptotic regions which are represented by special "points" in the complete conformal diagram. The redshift of signals emitted by particles which fall into the singularity, as detected by those observers which escape, is also calculated.

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arXiv1999

Smearing of chaos in sandwich pp-waves

Recent results demonstrating the chaotic behavior of geodesics in non-homogeneous vacuum pp-wave solutions are generalized. Here we concentrate on motion in non-homogeneous sandwich pp-waves and show that chaos smears as the duration of these gravitational waves is reduced. As the number of radial bounces of any geodesic decreases, the outcome channels to infinity become fuzzy, and thus the fractal structure of the initial conditions characterizing chaos is cut at lower and lower levels. In the limit of impulsive waves, the motion is fully non-chaotic. This is proved by presenting the geodesics in a simple explicit form which permits a physical interpretation, and demonstrates the focusing effect. It is shown that a circle of test particles is deformed by the impulse into a family of closed hypotrochoidal curves in the transversal plane. These are deformed in the longitudinal direction in such a way that a specific closed caustic surface is formed.

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arXiv1999

Nonexpanding impulsive gravitational waves with an arbitrary cosmological constant

Exact solutions for nonexpanding impulsive waves in a background with nonzero cosmological constant are constructed using a `cut and paste' method. These solutions are presented using a unified approach which covers the cases of de Sitter, anti-de Sitter and Minkowski backgrounds. The metrics are presented in continuous and distributional forms, both of which are conformal to the corresponding metrics for impulsive pp-waves, and for which the limit as $Λ\to 0$ can be made explicitly.

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arXiv1999

Gravitational waves in vacuum spacetimes with cosmological constant. I. Classification and geometrical properties of non-twisting type N solutions

All non-twisting Petrov-type N solutions of vacuum Einstein field equations with cosmological constant Lambda are summarized. They are shown to belong either to the non-expanding Kundt class or to the expanding Robinson-Trautman class. Invariant subclasses of each class are defined and the corresponding metrics are given explicitly in suitable canonical coordinates. Relations between the subclasses and their geometrical properties are analyzed. In the subsequent paper these solutions are interpreted as exact gravitational waves propagating in de Sitter or anti-de Sitter spacetimes.

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arXiv1999

Gravitational waves in vacuum spacetimes with cosmological constant. II. Deviation of geodesics and interpretation of non-twisting type N solutions

In a suitably chosen essentially unique frame tied to a given observer in a general spacetime, the equation of geodesic deviation can be decomposed into a sum of terms describing specific effects: isotropic (background) motions associated with the cosmological constant, transverse motions corresponding to the effects of gravitational waves, longitudinal motions, and Coulomb-type effects. Conditions under which the frame is parallelly transported along a geodesic are discussed. Suitable coordinates are introduced and an explicit coordinate form of the frame is determined for spacetimes admitting a non-twisting null congruence. Specific properties of all non-twisting type N vacuum solutions with cosmological constant Lambda (non-expanding Kundt class and expanding Robinson-Trautman class) are then analyzed. It is demonstrated that these spacetimes can be understood as exact transverse gravitational waves of two polarization modes "+" and "x", shifted by pi/4, which propagate "on" Minkowski, de Sitter, or anti-de Sitter backgrounds. It is also shown that the solutions with Lambda>0 may serve as exact demonstrations of the cosmic "no-hair" conjecture in radiative spacetimes with no symmetry.

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arXiv1999

Expanding impulsive gravitational waves

We explicitly demonstrate that the known solutions for expanding impulsive spherical gravitational waves that have been obtained by a "cut and paste" method may be considered to be impulsive limits of the Robinson-Trautman vacuum type N solutions. We extend these results to all the generically distinct subclasses of these solutions in Minkowski, de Sitter and anti-de Sitter backgrounds. For these we express the solutions in terms of a continuous metric. Finally, we also extend the class of spherical shock gravitational waves to include a non-zero cosmological constant.

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arXiv1999

Global structure of Robinson-Trautman radiative space-times with cosmological constant

Robinson-Trautman radiative space-times of Petrov type II with a non-vanishing cosmological constant Lambda and mass parameter m>0 are studied using analytical methods. They are shown to approach the corresponding spherically symmetric Schwarzschild-de Sitter or Schwarzschild-anti-de Sitter solution at large retarded times. Their global structure is analyzed, and it is demonstrated that the smoothness of the extension of the metrics across the horizon, as compared with the case Lambda=0, is increased for Lambda>0 and decreased for Lambda<0. For the extreme value 9Lambda m^2=1, the extension is smooth but not analytic. This case appears to be the first example of a smooth but not analytic horizon. The models with Lambda>0 exhibit explicitly the cosmic no-hair conjecture under the presence of gravitational waves.

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arXiv1998

Chaotic motion in pp-wave spacetimes

We investigate geodesics in non-homogeneous vacuum pp-wave solutions and demonstrate their chaotic behavior by rigorous analytic and numerical methods. For the particular class of solutions considered, distinct "outcomes" (channels to infinity) are identified, and it is shown that the boundary between different outcomes has a fractal structure. This seems to be the first example of chaos in exact radiative spacetimes.

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arXiv1998

Interpreting a conformally flat pure radiation space-time

A physical interpretation is presented of the general class of conformally flat pure radiation metrics that has recently been identified by Edgar and Ludwig. It is shown that, at least in the weak field limit, successive wave surfaces can be represented as null (half) hyperplanes rolled around a two-dimensional null cone. In the impulsive limit, the solution reduces to a pp-wave whose direction of propagation depends on retarded time. In the general case, there is a coordinate singularity which corresponds to an envelope of the wave surfaces. The global structure is discussed and a possible vacuum extension through the envelope is proposed.

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arXiv1998

Boosted static multipole particles as sources of impulsive gravitational waves

It is shown that the known solutions for nonexpanding impulsive gravitational waves generated by null particles of arbitrary multipole structure can be obtained by boosting the Weyl solutions describing static sources with arbitrary multipole moments, at least in a Minkowski background. We also discuss the possibility of boosting static sources in (anti-) de Sitter backgrounds, for which exact solutions are not known, to obtain the known solutions for null multipole particles in these backgrounds.

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arXiv1998

Non-expanding impulsive gravitational waves

We investigate a class of impulsive gravitational waves which propagate either in Minkowski or in the (anti-)de Sitter background. These waves are constructed as impulsive members of the Kundt class $P(Λ)$ of non-twisting, non-expanding type N solutions of vacuum Einstein equations with a cosmological constant $Λ$. We show that the only non-trivial waves of this type in Minkowski spacetime are impulsive pp-waves. For $Λ\not=0$ we demonstrate that the canonical subclasses of $P(Λ)$, which are invariantly different for smooth profiles, are all locally equivalent for impulsive profiles. Also, we present coordinate system for these impulsive solutions which is explicitly continuous.

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arXiv1998

Smooth sandwich gravitational waves

Gravitational waves which are smooth and contain two asymptotically flat regions are constructed from the homogeneous pp-waves vacuum solution. Motion of free test particles is calculated explicitly and the limit to an impulsive wave is also considered.

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arXiv1998

Chaos in pp-wave spacetimes

We demonstrate chaotic behavior of timelike, null and spacelike geodesics in non-homogeneous vacuum pp-wave solutions. This seems to be the first known example of a chaotic motion in exact radiative spacetime.

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arXiv1998

Continuous coordinates for all impulsive pp - waves

We present a coordinate system for a general impulsive gravitational pp - wave in vacuum in which the metric is explicitly continuous, synchronous and "transverse". Also, it is more appropriate for investigation of particle motions.

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arXiv1998

New examples of sandwich gravitational waves and their impulsive limit

Non-standard sandwich gravitational waves are constructed from the homogeneous pp vacuum solution and the motions of free test particles in the space-times are calculated explicitly. They demonstrate the caustic property of sandwich waves. By performing limits to impulsive gravitational wave it is demonstrated that the resulting particle motions are identical regardless of the ''initial'' sandwich.

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arXiv1998

Interpretation of the Siklos solutions as exact gravitational waves in the anti-de Sitter universe

The Siklos class of solutions of Einstein's field equations is investigated by analytical methods. By studying the behaviour of free particles we reach the conclusion that the space-times represent exact gravitational waves propagating in the anti-de Sitter universe. The presence of a negative cosmological constant implies that the 'background' space is not asymptotically flat and requires a 'rotating' reference frames in order to fully simplify and view the behaviour of nearby test particles. The Kaigorodov space-time, which is the simplest representative of the Siklos class, is analyzed in more detail. It is argued that it may serve as a 'cosmological' analogue of the well-known homogeneous pp-waves in the flat universe.

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