Relativistic Gravitational Field Research Articles

Persymmetric determinants 3:a basic determinant

The object of this paper is to list and prove a number of properties of the determinant K = ∥kij ∥n and its cofactors where with obvious restrictions on h. This determinant has been the subject of a number of short notes in the past but its importance has recently been enhanced by appearing in two papers on relativistic gravitational fields. Some of the 30 formulae and identities which are listed are therefore well-known but a significant number are new.

General relativistic gravitational field effects on superfluid phase interference devices

In some recent experiments, it has been established that the Newtonian gravitational potential can influence the phase interference between alternative virtual paths taken by a quantum test particle. The authors consider theoretically the influence of general relativistic fields on the phase interference of superfluid flows.

Finite homogeneous relativistic elastic sphere in its own gravitational field

This paper deals with static spherically symmetric elastic matter in its own relativistic gravitational field. It is shown that, in the case of a certain type of homogeneity, the field equations can be reduced to two ordinary nonlinear differential equations. These equations have solutions corresponding to finite bodies.

Constancy of the local velocity of light in general relativistic gravitational fields

Using the natural, real units (proper time and proper length) for the definition of the spatial velocity, it is shown that the velocity of light during its propagation through gravitational fields is constant and exactly equal to its value in vacuum. Therefore, according to General Relativity, it is not correct to speak about a variable velocity of light in gravitational fields.

Approximate Solutions of the Relativistic Gravitational Field Equations to Describe Clusters of Galaxies

Approximate solutions to the Einstein field equations are found which describe a spherically symmetric inhomogeneity in a general Robertson?Walker model, i.e. one with an arbitrary equation of state. The approximation hypothesis is that the pressure deviates only slightly from uniformity, and it is found that the density may have quite large local fluctuations, e.g. by a factor of 106 over a region 10-2 Mpc in diameter. Reference is made to observed data to determine which categories of stellar objects may be described by the results.

Systematic approximations in the calculation of gravitational fields

The determination of Newtonian gravitational fields is of trivial simplicity in comparison with corresponding relativistic problems. To find the Newtonian potential we do not have to solve any differential equation; it is given as an integral taken over the instantaneous mass distribution, and any difficulties there may be arise merely in evaluating the integral. In giving the well-known retarded-potential formula, Einstein (1916) took the first step towards the systematic calculation of relativistic gravitational fields. But it is only a first approximation, leaving in what purports to be empty space a residual energy tensor which is uncomfortably large. Further, the usual derivation of the retarded potential formula does not seem to open the way to higher approximations.