On the occurrence of naked singularities in general relativity

It is shown that spherically symmetric collapse can lead to singularities which arenot hidden within black holes.Work supported by the Deutsche Forschungsgemeinschaft.     

Method for analyzing coordinate singularities in the general theory of relativity

A general method for analyzing singularities of metrics is developed. Metrics are regularized and invariant operations are calculated, which must not change with regularization. This method is inspected in relation to the Schwarzschild metric.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 3, pp. 42–45, March, 1987.     

Investigation of singularities in general relativity

The problem of singularities for a non-symmetric and isentropic motion of a perfect fluid under the assumption of adiabatic thermodynamic processes is investigated from the standpoint of a local observer. It is shown that, whatever the distribution of matter might be, there occurred a singularity in the past in the non-rotating parts of the universe and it must occur again in the future if the universe is closed. It is further shown that the occurrence of a singularity in a rotating fluid seems inevitable, when the relativistic equation of state is considered, because of extremely high concentration of rest mass, though the possibility of its avoidance may not be ignored.     

On the occurrence of naked singularities in general relativity. II

It is shown that naked shell crossing singularities can occur in the gravitational collapse of a spherically symmetric ball of perfect fluid for a large family of equations of state in which the pressure has an (arbitrarily large) upper bound, and, moreover, that this behaviour is stable with respect to spherically symmetric perturbations of the initial data, as well as with respect to perturbations of the equation of state.Work supported by the Deutsche Forschungsgemeinschaft.     

Initial-value problems and singularities in general relativity

Linearized solution of Datta in a non-symmetric and isentropic motion of a perfect fluid is studied by dealing with a Cauchy problem in co-moving coordinates in the framework of general relativity. The problem of singularities is discussed from the standpoint of a local observer both for rotating and non-rotating fluids. It is shown that, whatever the distribution of matter, a singularity which occurred in the past in both the rotating and non-rotating parts of the universe must occur again later after some finite proper time, if the universe is closed. A modification is incorporated in Penrose’s theorem by explicitly exhibiting that the universe defined by Penrose can possess a Cauchy hypersurface.     

Republication of: On the general relativity theory

This English translation of the paper by H. Weyl, “Zur allgemeinen Relativitätstheorie”, Physikalische Zeitschrift 24, 230–232 (1923), in which he formulated the geometrical foundations of a model of an expanding Universe, has been selected by the Editors of General Relativity and Gravitation for publication in the Golden Oldies series of the journal. The paper is accompanied by an editorial note written by Juergen Ehlers and by Weyl’s brief biography compiled by Andrzej Krasiński from internet sources, with corrections provided by Weyl’s son and grandson.     

Investigation of the problem of singularities in general relativity

Recently Addy and Datta have obtained a linearized solution for isentropic motions of a perfect fluid by assigning Cauchy data on the hypersurfacex ⁴=0 and by imposing a restriction on the equation of state. In the present paper we pursue this study and discuss the problem of singularities from the standpoint of a local observer for which a singularity is defined as a state with an infinite proper rest mass density. It is shown that for a closed universe with any distribution of matter whatsoever there occurred a singularity in the past in the nonrotating parts of the universe and it must recur in the future. Furthermore, the collapse of a rotating fluid to a singularity seems inevitable when the relativistic equation of state is considered.     

Observables in the general theory of relativity

The theory of finite deviations of geodesics as directly observable variables in general relativity theory is elaborated in the proper coordinates of the reference frame of a solitary observer.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 7, pp. 80–83, July, 1976.     

On the mechanics of photon rockets in the general theory of relativity

Generally covariant equations of motion of a photon rocket comprising all the basic dynamic and thermodynamic processes are derived and are written for the case of a weak gravitational field. The equations lead to results which agree with those obtained by other means.     

ON the question of the uniqueness of the energy-momentum complex in the special and general theory of relativity

Modification of the Fock method is used to look systematically for the complexes of energy and momentum which are conserved as a consequence of the vacuum field equations of the second order (real and complex scalar field, real vector field, symmetric tensor field of the linearized and non-linear Einstein theory). In contrast to Fock's results for fields described by equations of the first order, the complexes are not defined uniquely. The non-uniquenesses are eliminated by supplementary conditions.This paper is based on a diploma thesis worked out at the Department of Theoretical Physics, Faculty of Mathematics and Physics, Charles University.     

Interacting fields in general relativity theory

The direct interaction of a massless neutral scalar field with an electromagnetic field is investigated with regard for the proper gravitational field. The interaction Lagrangian is chosen in the form L_int=FF, =e–1, where the parameter characterizes the interaction force. Exact static spherically and cylindrically symmetric solutions are obtained. A solution with a finite total field energy is extracted. A comparison is made with the corresponding system in flat space-time. It is concluded that the gravitational field performs a regulatory function.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 9, pp. 25–30, September, 1977.The authors are indebted to Yu. S. Vladimirov for valuable comments.     

Energy complex in the general theory of relativity

In the tetradic formulation of the theory of gravitation an energy complex is proposed which makes it possible to calculate unambiguously the energy enclosed in any volume, in any co-ordinate mesh, with an arbitrary orientation of local, Cartesian, three-dimensional frames. In deriving the complex the analogy between the tetradic equations of the gravitational field and the covariant form of the equations of electrodynamics is exploited. As an example, a number of exact solutions of the Einstein equations are considered.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii Fizika, No. 10, pp. 57–62, October, 1971.     

Plane waves in the general theory of relativity

The Newman-Penrose method is used to study the class of gravitational fields in a vacuum which permit a normal congruence of isotropic geodesies. The energy-momentum tensor is used in tetrad form to prove that if the nondegeneratemetric of these fields depends only on a single isotropic coordinate, the solutions will describe plane gravitational waves.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii Fizika, Vol. 12, No. 4, pp. 20–23, April, 1969.     

Kinetic equation in the general theory of relativity

An attempt is made to discover the physical content of the general-relativistic theory of gases. Under an invariant interpretation of the collision term, this theory does not satisfy the correspondence principle for classical theory. The collision term in the classical Boltzmann form is meaningful only in an isolated reference frame realized by a locally inertial frame with the origin at the collision point. With this formulation of the kinetic equations, the class of equilibrium states in GR expands considerably and also covers nonstationary distributions. A specific example of such a distribution that is locally Maxwellian is given.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 2, pp. 72–76, February, 1979.In conclusion, the author considers it his pleasant duty to thank Prof. N. A.Chernikov for useful discussion of certain problems touched on this paper, and A. V. Zakharov, who made this result of his article koown to the author.     

Electromagnetic radiation in the general theory of relativity

Spaces allowing a normal, shear-free, expanding congruence of isotropic geodesics are considered. A metric form allowing the simultaneous solution of the Einstein and Maxwell solutions for an isotropic electromagnetic field is derived in explicit form.Some of the nomenclature and definitions encountered in this paper were specified in Part I [1].Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 5, pp. 32–35, May, 1973.     

Gravitational waves in the general theory of relativity

The problem of gravitational radiation is discussed with the help of the Rodichev energy-momentum tensor. An invariant criterion is formulated for finding radiation in a space without sources. In general, the question of the presence of radiation in a system is resolved by a local study of the behavior of the energy-momentum tensor in the comoving tetrad. The results are applied to the study of certain exact solutions of the Einstein equations.     

Gravitational waves in the general theory of relativity

The methods and capabilities of the invariant theory of gravitational radiation derived previously are demonstrated for an exact solution of the Kaigorodov type III. Analysis of this solution shows that it describes gravitational radiation with sources.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii Fizika, No. 11, pp. 121–125, November, 1969.In conclusion, we thank V. I. Rodichev for constant interest in this study.