New classes of exact solutions for charged perfect fluids.

Abstract

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.