J Podolský

Impulsive waves in de Sitter and anti-de Sitter spacetimes generated by null particles with an arbitrary multipole structure

We describe a class of impulsive gravitational waves which propagate either in a de Sitter or an anti-de Sitter background. They are conformal to impulsive waves of Kundts class. In a background with positive cosmological constant they are spherical (but non-expanding) waves generated by pairs of particles with arbitrary multipole structure propagating in opposite directions. When the cosmological constant is negative, they are hyperboloidal waves generated by a null particle of the same type. In this case, they are included in the impulsive limit of a class of solutions described by Siklos that are conformal to pp-waves.

A note on the parameters of the Kerr-NUT-(anti-) de Sitter spacetime

Different forms of the metric for the Kerr–NUT–(anti-)de Sitter spacetime are being widely used in its extension to higher dimensions. The purpose of this note is to relate the parameters that are being used to the physical parameters (mass, rotation, NUT and cosmological constant) in the basic four-dimensional situation.

Global aspects of accelerating and rotating black hole spacetimes

The complete family of exact solutions representing accelerating and rotating black holes with possible electromagnetic charges and a NUT parameter is known in terms of a modified Plebanski–Demianski metric. This demonstrates the singularity and horizon structure of the sources but not that the complete spacetime describes two causally separated black holes. To demonstrate this property, the metric is first cast in the Weyl–Lewis–Papapetrou form. After extending this up to the acceleration horizon, it is then transformed to the boost-rotation-symmetric form in which the global properties of the solution are manifest. The physical interpretation of these solutions is thus clarified.

The global existence, uniqueness and 1-regularity of geodesics in nonexpanding impulsive gravitational waves

We study geodesics in the complete family of nonexpanding impulsive gravitational waves propagating in spaces of constant curvature, that is Minkowski, de Sitter and anti-de Sitter universes. Employing the continuous form of the metric we prove existence and uniqueness of continuously dierentiable geodesics (in the sense of Filippov) and use a C 1 -matching procedure to explicitly derive their form.

Static and radiating p-form black holes in the higher dimensional Robinson-Trautman class

A bstractWe study Robinson-Trautman spacetimes in the presence of an aligned p-form Maxwell field and an arbitrary cosmological constant in n ≥ 4 dimensions. As it turns out, the character of these exact solutions depends significantly on the (relative) value of n and p. In odd dimensions the solutions reduce to static black holes dressed with an electric and a magnetic field, with an Einstein space horizon (further constrained by the Einstein-Maxwell equations) — both the Weyl and Maxwell types are D. Even dimensions, however, open up more possibilities. In particular, when 2p = n there exist non-static solutions describing black holes gaining (or losing) mass by receiving (or emitting) electromagnetic radiation. In this case the Weyl type is II (D) and the Maxwell type can be II (D) or N. Conditions under which the Maxwell field is self-dual (for odd p) are also discussed, and a few explicit examples presented. Finally, the case p = 1 is special in all dimensions and leads to static metrics with a non-Einstein transverse space.

Physical interpretation of Kundt spacetimes using geodesic deviation

We investigate the fully general class of non-expanding, non-twisting and shear-free D-dimensional geometries using the invariant form of geodesic deviation equation which describes the relative motion of free test particles. We show that the local effect of such gravitational fields on the particles basically consists of isotropic motion caused by the cosmological constant Lambda, Newtonian-type tidal deformations typical for spacetimes of algebraic type D or II, longitudinal motion characteristic for spacetimes of type III, and type N purely transverse effects of exact gravitational waves with D(D-3)/2 polarizations. We explicitly discuss the canonical forms of the geodesic deviation motion in all algebraically special subtypes of the Kundt family for which the optically privileged direction is a multiple Weyl aligned null direction (WAND), namely D(a), D(b), D(c), D(d), III(a), III(b), IIIi, IIi, II(a), II(b), II(c) and II(d). We demonstrate that the key invariant quantities determining these algebraic types and subtypes also directly determine the specific local motion of test particles, and are thus measurable by gravitational detectors. As an example, we analyze an interesting class of type N or II gravitational waves which propagate on backgrounds of type O or D, including Minkowski, Bertotti-Robinson, Nariai and Plebanski-Hacyan universes.

Geodesic motion in Kundt spacetimes and the character of the envelope singularity

We investigate geodesics in specific Kundt type N (or conformally flat) solutions to Einsteins equations. Components of the curvature tensor in parallelly transported tetrads are then explicitly evaluated and analysed. This elucidates some interesting global properties of the spacetimes, such as an inherent rotation of the wave-propagation direction, or the character of singularities. In particular, we demonstrate that the characteristic envelope singularity of the rotated wave fronts is a (non-scalar) curvature singularity, although all scalar invariants of the Riemann tensor vanish there.

Absence of gyratons in the Robinson-Trautman class

We present the Riemann and Ricci tensors for a fully general non-twisting and shear-free geometry in arbitrary dimension D. This includes both the non-expanding Kundt and expanding Robinson-Trautman family of spacetimes. As an interesting application of these explicit expressions we then integrate the Einstein equations and prove a surprising fact that in any D the Robinson-Trautman class does not admit solutions representing gyratonic sources, i.e., matter field in the form of a null fluid (or particles propagating with the speed of light) with an additional internal spin. Contrary to the closely related Kundt class and pp-waves, the corresponding off-diagonal metric components thus do not encode the angular momentum of some gyraton. Instead, we demonstrate that in standard D=4 general relativity they directly determine two independent amplitudes of the Robinson-Trautman exact gravitational waves.

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

We analyse the directional properties of general gravitational, electromagnetic and spin-s fields near conformal infinity . The fields are evaluated in normalized tetrads which are parallelly propagated along null geodesics which approach a point P of . 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 ? > 0) or timelike (for ? 0 the radiation vanishes only along directions which are opposite to principal null directions. For ? < 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 .The directional structure of radiation near (anti-)de Sitter-like infinities supplements the standard peeling-off property of spin-s fields. This characterization offers a better understanding of the asymptotic behaviour of the fields near conformal infinity under the presence of a cosmological constant.

Interpreting a conformally flat pure radiation spacetime

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.