arXiv subjects

Jiri Bicak

Publications and source records attributed to Jiri Bicak.

At least 37 records · Page 2Linked to original sources

arXiv2007

Energy and angular momentum densities of stationary gravity fields

We give physical explanations of explicit invariant expressions for the energy and angular momentum densities of gravitational fields in stationary space-times. These expressions involve non-locally defined conformal factors. In certain coordinates these become locally defined in terms of the metric. These results are derived via expressions for total gravitational potential energy from the difference between the total energy and the mechanical energy. The latter involves kinetic energy seen in the frame of static observers. When in the axially symmetric case we consider zero angular momentum observers (who move orthogonally to surfaces of constant time), we find that the angular momentum they attribute to the gravitational field is solely due to their motion.

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arXiv2006

Gravitational energy in stationary spacetimes

Static observers remain on Killing-vector world lines and measure the rest-mass+kinetic energies of particles moving past them, and the flux of that mechanical energy through space and time. The total mechanical energy is the total flux through a spacelike cut at one time. The difference between the total mass-energy and the total mechanical energy is the total gravitational energy, which we prove to be negative for certain classes of systems. For spherical systems, Misner, Thorne and Wheeler define the total gravitational energy this way. To obtain the gravitational energy density analogous to that of electromagnetism we first use Einstein's equations with integrations by parts to remove second order derivatives. Next we apply a conformal transformation to reexpress the scalar 3-curvature of the 3-space. The resulting density is non-local. We repeat the argument for mechanical energies as measured by stationary observers moving orthogonally to constant time slices like the "zero angular momentum" observers of Bardeen who exist even within ergospheres.

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arXiv2006

Einstein equations: exact solutions

In Einstein's general relativity, with its nonlinear field equations, the discoveries and analyzes of various specific explicit solutions made a great impact on understanding many of the unforeseen features of the theory. Some solutions found fundamental applications in astrophysics, cosmology and, more recently, in the developments inspired by string theory. In this short article we survey the invariant characterization and classification of the solutions and describe the properties and role of the most relevant classes: Minkowski, (anti-)de Sitter spacetimes, spherical Schwarzschild and Reissner-Nordstroem metrics, stationary axisymmetric solutions, radiative metrics describing plane and cylindrical waves, radiative fields of uniformly accelerated sources and Robinson-Trautman solutions. Metrics representing regions of spacetimes filled with matter are also discussed and cosmological models are very briefly mentioned. Some parts of the text are based on a detailed survey which appeared in gr-qc/0004016 (see Ref. 2).

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arXiv2006

Ultrarelativistic sources in nonlinear electrodynamics

The fields of rapidly moving sources are studied within nonlinear electrodynamics by boosting the fields of sources at rest. As a consequence of the ultrarelativistic limit the delta-like electromagnetic shock waves are found. The character of the field within the shock depends on the theory of nonlinear electrodynamics considered. In particular, we obtain the field of an ultrarelativistic charge in the Born-Infeld theory.

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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.

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arXiv2005

Relativistic conservation laws and integral constraints for large cosmological perturbations

For every mapping of a perturbed spacetime onto a background and with any vector field $ξ$ we construct a conserved covariant vector density $I(ξ)$, which is the divergence of a covariant antisymmetric tensor density, a "superpotential". $ I(ξ)$ is linear in the energy-momentum tensor perturbations of matter, which may be large; $I(ξ)$ does not contain the second order derivatives of the perturbed metric. The superpotential is identically zero when perturbations are absent. By integrating conserved vectors over a part $\Si$ of a hypersurface $S$ of the background, which spans a two-surface $\di\Si$, we obtain integral relations between, on the one hand, initial data of the perturbed metric components and the energy-momentum perturbations on $\Si$ and, on the other hand, the boundary values on $\di\Si$. We show that there are as many such integral relations as there are different mappings, $ξ$'s, $\Si$'s and $\di\Si$'s. For given boundary values on $\di\Si$, the integral relations may be interpreted as integral constraints (e.g., those of Traschen) on local initial data including the energy-momentum perturbations. Conservation laws expressed in terms of Killing fields $\Barξ$ of the background become "physical" conservation laws. In cosmology, to each mapping of the time axis of a Robertson-Walker space on a de Sitter space with the same spatial topology there correspond ten conservation laws. The conformal mapping leads to a straightforward generalization of conservation laws in flat spacetimes. Other mappings are also considered. ...

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arXiv2005

On the uniqueness of harmonic coordinates

Harmonic coordinate conditions in stationary asymptotically flat spacetimes with matter sources have more than one solution. The solutions depend on the degree of smoothness of the metric and its first derivatives, which we wish to impose across the material boundary, and on the conditions at infinity and at a suitable point inside the matter. This is illustrated in detail by simple fully solvable examples of static spherically symmetric spacetimes in global harmonic coordinates. Examples of stationary electrovacuum spacetimes described simply in harmonic coordinates are also given. They can represent the exterior fields of material discs. The use of an appropriate background metric considerably simplifies the calculations.

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arXiv2003

Do Rotations Beyond the Cosmological Horizon Affect the Local Inertial Frame?

If perturbations beyond the horizon have the velocities prescribed everywhere then the dragging of inertial frames near the origin is suppressed by an exponential factor. However if perturbations are prescribed in terms of their angular momenta there is no such suppression. We resolve this paradox and in doing so give new explicit results on the dragging of inertial frames in closed, flat and open universe with and without a cosmological constant.

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arXiv2003

Toroidal Perturbations of Friedmann-Robertson-Walker Universes

Explicit expressions are found for the axisymmetric metric perturbations of the closed, flat and open FRW universes caused by toroidal motions of the cosmic fluid. The perturbations are decomposed in vector spherical harmonics on 2-spheres, but the radial dependence is left general. Solutions for general odd-parity $l$-pole perturbations are given for either angular velocities or angular momenta prescribed. In particular, in case of closed universes the solutions require a special treatment of the Legendre equation.

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arXiv2003

Gauge-invariant Hamiltonian dynamics of cylindrical gravitational waves

The model of cylindrical gravitational waves is employed to work out and check a recent proposal in Ref. [11] how a diffeomorphism-invariant Hamiltonian dynamics is to be constructed. The starting point is the action by Ashtekar and Pierri because it contains the boundary term that makes it differentiable for non-trivial variations at infinity. With the help of parametrization at infinity, the notion of gauge transformation is clearly separated from that of asymptotic symmetry. The symplectic geometry of asymptotic symmetries and asymptotic time is described and the role of the asymptotic structures in defining a zero-motion frame for the Hamiltonian dynamics of Dirac observables is explained. Complete sets of Dirac observables associated with the asymptotic fields are found and the action of the asymptotic symmetries on them is calculated. The construction of the corresponding quantum theory is sketched: the Fock space, operators of asymptotic fields, the Hamiltonian and the scattering matrix are determined.

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arXiv2003

Canonical theory of spherically symmetric spacetimes with cross-streaming null dusts

The Hamiltonian dynamics of two-component spherically symmetric null dust is studied with regard to the quantum theory of gravitational collapse. The components--the ingoing and outgoing dusts--are assumed to interact only through gravitation. Different kinds of singularities, naked or "clothed", that can form during collapse processes are described. The general canonical formulation of the one-component null-dust dynamics by Bicak and Kuchar is restricted to the spherically symmetric case and used to construct an action for the two components. The transformation from a metric variable to the quasilocal mass is shown to simplify the mathematics. The action is reduced by a choice of gauge and the corresponding true Hamiltonian is written down. Asymptotic coordinates and energy densities of dust shells are shown to form a complete set of Dirac observables. The action of the asymptotic time translation on the observables is defined but it has been calculated explicitly only in the case of one-component dust (Vaidya metric).

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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.

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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^-.

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arXiv2002

Notes on static cylindrical shells

Static cylindrical shells made of various types of matter are studied as sources of the vacuum Levi-Civita metrics. Their internal physical properties are related to the two essential parameters of the metrics outside. The total mass per unit length of the cylinders is always less than 1/4. The results are illustrated by a number of figures.

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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.

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arXiv2002

Radiative spacetimes

The question of existence of general, asymptotically flat radiative spacetimes and examples of explicit classes of radiative solutions of Einstein's field equations are discussed in the light of some new developments. The examples are cylindrical waves, Robinson-Trautman and type N spacetimes and especially boost-rotation symmetric spacetimes representing uniformly accelerated particles or black holes.

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arXiv2002

Exact solutions and their interpretation

This is the account of the workshop Exact solutions and their interpretation at the 16-th International Conference on General Relativity and Gravitation held in Durban, July 15-21, 2001. Work reported in 32 oral contributions spanned a wide variety of topics, ranging from exact radiative spacetimes to cosmological solutions. Two invited review talks, on the role of exact solutions in string theory and in cosmology, are also described.

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arXiv2001

Black Holes under External Influence

The work on black holes immersed in external fields is reviewed in both test-field approximation and within exact solutions. In particular we pay attention to the effect of the expulsion of the flux of external fields across charged and rotating black holes which are approaching extremal states. Recently this effect has been shown to occur for black hole solutions in string theory. We also discuss black holes surrounded by rings and disks and rotating black holes accelerated by strings.

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