arXiv subjects

Pavel Krtous

Publications and source records attributed to Pavel Krtous.

52 records · Page 3Linked to original sources

arXiv2006

Electromagnetic field near cosmic string

The retarded Green function of the electromagnetic field in spacetime of a straight thin cosmic string is found. It splits into a geodesic part (corresponding to the propagation along null rays) and to the field scattered on the string. With help of the Green function the electric and magnetic fields of simple sources are constructed. It is shown that these sources are influenced by the cosmic string through a self-interaction with their field. The distant field of static sources is studied and it is found that it has a different multipole structure than in Minkowski spacetime. On the other hand, the string suppresses the electric and magnetic field of distant sources--the field is expelled from regions near the string.

gr-qc↗

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.

gr-qc↗

arXiv2006

Fields of accelerated sources: Born in de Sitter

This paper deals thoroughly with the scalar and electromagnetic fields of uniformly accelerated charges in de Sitter spacetime. It gives details and makes various extensions of our Physical Review Letter from 2002. The basic properties of the classical Born solutions representing two uniformly accelerated charges in flat spacetime are first summarized. The worldlines of uniformly accelerated particles in de Sitter universe are defined and described in a number of coordinate frames, some of them being of cosmological significance, the other are tied naturally to the particles. The scalar and electromagnetic fields due to the accelerated charges are constructed by using conformal relations between Minkowski and de Sitter space. The properties of the generalized `cosmological' Born solutions are analyzed and elucidated in various coordinate systems. In particular, a limiting procedure is demonstrated which brings the cosmological Born fields in de Sitter space back to the classical Born solutions in Minkowski space. In an extensive Appendix, which can be used independently of the main text, nine families of coordinate systems in de Sitter spacetime are described analytically and illustrated graphically in a number of conformal diagrams.

gr-qc↗

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.

gr-qc↗

arXiv2005

Accelerated black holes in an anti-de Sitter universe

The C-metric is one of few known exact solutions of Einstein's field equations which describes the gravitational field of moving sources. For a vanishing or positive cosmological constant, the C-metric represents two accelerated black holes in asymptotically flat or de Sitter spacetime. For a negative cosmological constant the structure of the spacetime is more complicated. Depending on the value of the acceleration, it can represent one black hole or a sequence of pairs of accelerated black holes in the spacetime with an anti-de Sitter-like infinity. The global structure of this spacetime is analyzed and compared with an empty anti-de Sitter universe. It is illustrated by 3D conformal-like diagrams.

gr-qc↗

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.

gr-qc↗

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.

gr-qc↗

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.

gr-qc↗

arXiv2003

Radiation from accelerated black holes in de Sitter universe

Radiative properties of gravitational and electromagnetic fields generated by uniformly accelerated charged black holes in asymptotically de Sitter spacetime are studied by analyzing the C-metric exact solution of the Einstein-Maxwell equations with a positive cosmological constant. Its global structure and physical properties are thoroughly discussed. We explicitly find and describe the specific pattern of radiation which exhibits the dependence of the fields on a null direction along which the (spacelike) conformal infinity is approached. This directional characteristic of radiation supplements the peeling behavior of the fields near the infinity. The interpretation of the solution is achieved by means of various coordinate systems, and suitable tetrads. Relation to the Robinson-Trautman framework is also presented.

gr-qc↗

arXiv2003

Radiation from accelerated black holes in an anti-de Sitter universe

We study gravitational and electromagnetic radiation generated by uniformly accelerated charged black holes in anti-de Sitter spacetime. This is described by the C-metric exact solution of the Einstein-Maxwell equations with a negative cosmological constant Lambda. We explicitly find and interpret the pattern of radiation that characterizes the dependence of the fields on a null direction from which the (timelike) conformal infinity is approached. This directional pattern exhibits specific properties which are more complicated if compared with recent analogous results obtained for asymptotic behavior of fields near a de Sitter-like infinity. In particular, for large acceleration the anti-de Sitter-like infinity is divided by Killing horizons into several distinct domains with a different structure of principal null directions, in which the patterns of radiation differ.

gr-qc↗

arXiv2003

Gravitational and electromagnetic fields near an anti-de Sitter-like infinity

We analyze asymptotic structure of general gravitational and electromagnetic fields near an anti-de Sitter-like conformal infinity. Dependence of the radiative component of the fields on a null direction along which the infinity is approached is obtained. The directional pattern of outgoing and ingoing radiation, which supplements standard peeling property, is determined by the algebraic (Petrov) type of the fields and also by orientation of principal null directions with respect to the timelike infinity. The dependence on the orientation is a new feature if compared to spacelike infinity.

gr-qc↗

arXiv2003

Boundary Quantum Mechanics

A reformulation of a physical theory in which measurements at the initial and final moments of time are treated independently is discussed, both on the classical and quantum levels. Methods of the standard quantum mechanics are used to quantize boundary phase space to obtain boundary quantum mechanics -- a theory that does not depend on the distinction between the initial and final moments of time, a theory that can be formulated without reference to the causal structure. As a supplementary material, the geometrical description of quantization of a general (e.g. curved) configuration space is presented.

quant-ph↗

arXiv2003

Gravitational and electromagnetic fields near a de Sitter-like infinity

We present a characterization of general gravitational and electromagnetic fields near de Sitter-like conformal infinity which supplements the standard peeling behavior. This is based on an explicit evaluation of the dependence of the radiative component of the fields on the null direction from which infinity is approached. It is shown that the directional pattern of radiation has a universal character that is determined by the algebraic (Petrov) type of the spacetime. Specifically, the radiation field vanishes along directions opposite to principal null directions.

gr-qc↗

arXiv2002

The fields of uniformly accelerated charges in de Sitter spacetime

The scalar and electromagnetic fields of charges uniformly accelerated in de Sitter spacetime are constructed. They represent the generalization of the Born solutions describing fields of two particles with hyperbolic motion in flat spacetime. In the limit Lambda -> 0, the Born solutions are retrieved. Since in the de Sitter universe the infinities I^+- are spacelike, the radiative properties of the fields depend on the way in which a given point of I^+- is approached. The fields must involve both retarded and advanced effects: Purely retarded fields do not satisfy the constraints at the past infinity I^-.

gr-qc↗

arXiv2002

Accelerated sources in de Sitter spacetime and the insufficiency of retarded fields

The scalar and electromagnetic fields produced by the geodesic and uniformly accelerated discrete charges in de Sitter spacetime are constructed by employing the conformal relation between de Sitter and Minkowski space. A special attention is paid to new effects arising in spacetimes which, like de Sitter space, have spacelike conformal infinities. Under the presence of particle and event horizons, purely retarded fields (appropriately defined) become necessarily singular or even cannot be constructed at the "creation light cones" -- future light cones of the "points" at which the sources "enter" the universe. We construct smooth (outside the sources) fields involving both retarded and advanced effects, and analyze the fields in detail in case of (i) scalar monopoles, (ii) electromagnetic monopoles, and (iii) electromagnetic rigid and geodesic dipoles.

gr-qc↗

arXiv2000

Sum-Over-Histories Quantization of Relativistic Particle

Sum-over-histories quantization of particle-like theory in curved space is discussed. It is reviewed that the propagator satisfies the Schrodinger equation respective wave equation with a Laplace-like operator. The exact dependence of the operator on the choice of measure is shown. Next, modifications needed for a manifold with a boundary are introduced, and the exact form of the equation for the propagator is derived. It is shown that the Laplace-like operator contains some distributional terms localized on the boundary. These terms induce proper boundary conditions for the propagator. This choice of boundary conditions is explained as a consequence of a measurement of particles on the boundary. The interaction with sources inside of the domain and sources on the boundary is also discussed.

gr-qc↗