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

Abstract

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.