Charged fluid sphere in general relativity

Abstract

An analytic solution of the relativistic field equations is obtained for a static, spherically symmetric distribution of charged fluid. The arbitrary constants are determined by matching it with the Reissner–Nordström solution over the boundary. The distribution behaves like a charged perfect gas. As a particular case a solution for a spherical distribution of charged incoherent matter is deduced where the charge density and the mass density are equal in magnitude. In the absence of the charge, the solution reduces to Tolman’s solution VI with B=0.