Abstracts Mathematics

New classes of exact solutions for charged perfect fluids.

by Thulani Richard. Mthethwa

We investigate techniques to generate new classes of exact solutions to the Einstein- Maxwell field equations which represent the gravitational field of charged perfect fluid spherically symmetric distributions of matter. Historically, a large number of solutions have been proposed but only a small number have been demonstrated to satisfy elementary conditions for physical acceptability. Firstly we examine the case of the constant density and constant electric field charged fluid sphere and show empirically that such configurations of matter are unlikely to exist as basic physical requirements are violated. We then make an ansatz relating the fluid's electric field intensity to one of the gravitational potentials thereby simplifying the system of partial differential equations. This prescription yields an algorithmic process to generate new classes of exact solutions. We present a number of new solutions and comment on their viability as stellar models. Graphical plots generated by symbolic software of the main dynamical and geometrical quantities verify that one of our models is suitable to represent a physically relevant distribution of charged matter in the form of a spherical shell. In particular, positive definiteness of energy density and pressure are guaranteed, a pressure free hypersurface denoting the boundary of the star exists, the sound speed is shown to be sub-luminal and the energy conditions are satisfied everywhere in the interior of the star.