The general solution for spherical charged dust

Abstract

The general solution of the Maxwell-Einstein equations for spherical charged dust flow is presented explicitly. The solution is first derived, by a simple geometrical construction, in mass-area (m, r) coordinates, and then transformed to mass-proper time (m, tau ) coordinates. This solution depends on three arbitrary functions of the mass coordinate. This is just what one would expect because, in general, three arbitrary functions are required to determine the evolution of charged dust spheres, namely the initial distributions of the velocity, matter density and charge density. The generalisation to the case of non-zero cosmological constant is also presented. In the special case of neutral dust (and without a cosmological constant) the charged-dust solution reduces to the Tolman-Bondi solution. Several general properties are discussed, as well as two special subclasses-the marginally bound case and the self-similar case.