Generating Einstein’s solutions via hypergeometric equation

Abstract

Exact solutions to Einstein field equations in spherically symmetric gravitational fields are obtained for an anisotropic matter with specified forms for the anisotropic factor and one of the gravitational potentials. The solution of the Einstein field equations is reduced to a difference equation with variable rational coefficients which can be solved in general. It is possible to obtain general class of solutions in terms of special functions and elementary functions for different partial geometries.