A. K. Raychaudhuri

Static electromagnetic fields in general relativity

Abstract The paper presents the solutions of the equations of Rainichs “already unified theory” for the case when the field is static and the diagonalized metric tensor components are functions of one coordinate alone. Although the solutions obtained occur already in the literature, the new approach seems interesting and it is proposed to extend the investigation to more complicated cases.

Static Distribution of Charged Dust in General Relativity

The paper considers charged dust distributions in equilibrium. If the dust be uniformly charged (i. e. if the ratio of the charge density to the matter density be constant) or if the surfaces of the dust distributions be equipotential surfaces and inside these surfaces there is no hole or pocket of alien matter, then there exists a simple relation between and g00and ϕ, the electrostatic potential and the charge density must be equal to the matter density. Further in this case, the whole system of field equations can be reduced to a single Laplace equation in the empty space outside and to a nonlinear modified Poisson equation within the charged dust distributions.

Tachyons and gravitation

This note presents the following results: (1) In the weak field approximation, the tachyon apparently experiences a repulsion due to ordinary matter; (2) a tachyon turns back from a black hole after penetrating the Schwarzschild singularity; (3) in ever expanding isotropic universes the tachyon velocity becomes arbitrarily large at a finite time; (4) between tachyons themselves, there is apparently an attraction.

Conformal flatness and the Schwarzschild interior solution

The paper gives a rigorous proof of the theorem that the only static conformally flat metric for a perfect fluid distribution is the Schwarzschild interior metric.

Viscous fluid interpretation of electromagnetic fields. II

As observed by Tupper, if the Ricci tensor satisfies the Rainich conditions for a nonnull electromagnetic field, the energy stress tensor may sometimes be interpreted as due to a viscous fluid (apparently Tupper believed this to be possible for all electrovac solutions). The present paper shows that for such an interpretation to be possible, there must be an additional symmetry property. Even then in some cases the interpretation may not work due to unacceptable behavior of the fluid velocity vector.

Stationary cylindrically symmetric clusters of particles in general relativity

The case of a cylindrically symmetric cluster of particles moving in circles perpendicular to the axis of symmetry is discussed on the basis of the equations of general relativity. A number of special solutions are obtained, and two interesting results on the relation between the gravitational mass and the sum of the free particle masses for these clusters are deduced.

Field of a Charged Particle in Brans-Dicke Theory

In case of a vacuum electrostatic field in Brans-Dicke theory, by assuming a functional relationship between g 00 and the electrostatic potential φ, it is shown that g 00 ψ= φ 2 +aφ+b, where ψ is the scalar of B-D theory and the relation holds irrespective of any symmetry requirement. The B-D field equations are completely solved for the spherically symmetric field of a charged particle. The nature of the singularities is found to differ from that in the Reissner-Nordstrom solution.

Stationary electromagnetic fields in general relativity

The paper presents some solutions of the Einstein‐Maxwell equations corresponding to a superposed electric and magnetic field at right angles to each other. The solutions are stationary and include the case of null field also. There are, however, some singularities in the metric tensor.

Singularity-Free Cosmological Solutions with Non-Rotating Perfect Fluids

The paper establishes the result that solutions of the type described in the title of the article are in essence only those that have been already presented in the literature provided the acceleration vector is hypersurface orthogonal. The procedure adopted in the paper is somewhat novel - while the usual practice is to display an exact solution and then to examine whether it is singularity free, the present paper discovers the conditions which a singularity free solution of the desired type must satisfy. There is no attempt to obtain exact solutions. Simply, the conditions that were ad-hoc introduced in the deduction of singularity free solutions are here shown to follow from the requirement of non-singularity.

Temperature dependent gravitational constant and black hole physics

This letter examines the thermodynamics of black holes in case of a varying gravitational constant. We find that the second law of thermodynamics may remain valid contrary to the opinions expressed by some.