Interacting electromagnetic shock waves in general relativity

It is shown that the continuity conditions of Lichnerowicz must generally be relaxed in favour of the O'Brien-Synge conditions in the case of shock electromagnetic waves. This is in particular true when two electromagnetic shock waves are in collision. Gravitational impulse waves are produced as a result of the weakened conditions. An exact solution exhibiting this behaviour is derived, and the effect of the impulse waves on a measuring device are compared with experimental results of Weber.     

Cosmological models in general relativity

LRS Bianchi type-I space-time filled with perfect fluid is considered here with deceleration parameter as variable. The metric potentialsA andB are functions of x as well as t. Assuming B′/B = f (x), where prime denotes differentiation with respect to x, it was found thatA = (l′/l)B andB = lS(t), wherel = f (x) andS is the scale factor which is a function of t only. The value of Hubble’s constantH ₀ was found to be less than half for non-flat model and is equal to 1.3 for a flat model     

Interacting electromagnetic waves in general relativity

The problem is considered of finding exact solutions of the Einstein-Maxwell equations which describe the physical situation of two colliding and subsequently interacting electromagnetic waves. The general theory of relativity predicts a nonlinear interaction between electromagnetic waves. The situation is described using an approximate geometrical method, and a new exact solution describing two interacting electromagnetic waves is given. This describes waves emitted from two sources mutually focusing each other on the opposite source.     

Analyzing gravitational waves with general relativity

After a short review of prominent properties of gravitational waves and of the newly born gravitational astronomy, we focus on theoretical aspects. Analytic approximation methods in general relativity have played a crucial role in the recent discoveries of gravitational waves. They are used to build theoretical template banks for searching and analyzing the signals in the ground-based detectors LIGO and Virgo, and, further ahead, space-based LISA-like detectors. In particular, the post-Newtonian approximation describes with high accuracy the early inspiral of compact binary systems, made of black holes or neutron stars. It mainly consists of extending the Einstein quadrupole formula by a series of relativistic corrections up to high order. The compact objects are modeled by point masses with spins. The practical calculations face difficult problems of divergences, which have been solved thanks to dimensional regularization. In the last rotations before the merger, the finite size effects and the internal structure of neutron stars (notably the internal equation of state) affect the evolution of the orbit and the emission of gravitational waves. We describe these effects within a simple Newtonian model.     

Cosmological special relativity

Recently we presented a new special relativity theory for cosmology in which it was assumed that gravitation can be neglected and thus the bubble constant can be taken as a constant. The theory was presented in a six-dimensional hvperspace. three for the ordinary space and three for the velocities. In this paper we reduce our hyperspace to four dimensions by assuming that the three-dimensional space expands only radially, thus one is left with the three dimensions of ordinary space and one dimension of the radial velocity.     

Cosmological application on five-dimensional teleparallel theory equivalent to general relativity

A theory of(4+1)-dimensional gravity has been developed on the basis of which equivalent to the theory of general relativity by teleparallel.The fundamental gravitational field variables are the 5-dimensional(5D) vector fields(pentad),defined globally on a manifold M,and gravity is attributed to the torsion.The Lagrangian density is quadratic in the torsion tensor.We then apply the field equations to two different homogenous and isotropic geometric structures which give the same line element,i.e.,FRW in five dimensions.The cosmological parameters are calculated and some cosmological problems are discussed.     

Cosmological models in general relativity and brans-dicke theories: a comparison

We review general relativistic and Brans-Dicke cosmological models of the early universe and for the present phase. Both theories render similar results, in general, as far as Mach's principle is concerned. There is some difference in the stability problem for the inflationary phase, and we point out how to test one theory against the other experimentally.     

The velocity of magnetohydrodynamic waves in general relativity

The energy-momentum tensor for a perfect fluid with infinite conductivity is modified slightly by attributing a proper energy content to a field of tension, as proposed by Cattaneo, for a perfect nonconducting fluid, and it is shown that with this modification the velocities of the hydrodynamic waves in the fluid do not exceed C. This contrasts with the standard theory in which a lower limit must be placed on the compressibility of the fluid to prevent the velocity of the ‘fast’ hydrodynamic wave fron exceeding c. The velocity of the Alfvén wave is changed only slightly and is always less than c as in the standard theory.     

The collision of plane waves in general relativity

A number of exact solutions of Einstein's equations are obtained, which describe the collision and subsequent interaction of two plane parallel waves. Gravitational waves, null electromagnetic fields, and neutrino fields are all considered with collisions between any two types. It is shown that two such waves mutually focus each other with the focus usually appearing as a singularity in space-time. Further conclusions are made regarding the qualitative nature of the interactions, and it is argued that these also apply in more realistic physical situations.     

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.     

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.     

Cosmological solutions foe a spinor field in the general theory of relativity

We consider models of the universe containing linear and nonlinear spinor matter. It is assumed that the linear spinor matter is described by the generally covariant Dirac equation, and the nonlinear by the generally covariant Ivanenko-Heisenberg equation.Translated from Izvestiya VUZ. Fizika, No. 12, pp. 68–71, December, 1973.     

On the superposition of electromagnetic waves in general relativity

It is shown that, in a region of space-time containing two independent electromagnetic waves propagating in different directions, it is not possible for the two waves to follow simultaneously affinely parameterised shear-free and twist-free null geodesic congruences.     

An impossible superposition of electromagnetic waves in general relativity

This paper presents an example, similar to but distinct from one given in 1975 by Griffiths, of an insoluble problem on the superposition of a pair of electromagnetic waves.