Class of solutions of Einstein's field equations for static fluid spheres

Abstract

In this paper we solve the field equations of general relativity for a static, spherically symmetric material distribution and present a class of new analytic solutions describing perfect fluid spheres. In general, the pressure and density diverge at the center, while their ratio remains finite. Each solution has a maximum mass which is less than $\frac{(\sqrt{2}\ensuremath{-}1)}{(2\sqrt{2}\ensuremath{-}1)}$ times the radius of the sphere. The solution is a generalization of Tolman's I, IV, and V solutions and the de Sitter solution. As a special case, another class of new analytic solutions is derived which has an equation of state. The existence of a class of solutions describing gaseous distributions has also been established.