Analysis of a charged Schwarzschild sphere

We obtain a solution of the Einstein-Maxwell field equations which reduces to the Schwarzschild interior solution in the absence of the electrostatic field. A form for one of the gravitational potentials and the electric field intensity are selected in order to integrate the field equations. The solution is shown to be equivalent to the Schwarzschild solution in the absence of charge. The pressure vanishes for a certain radius and the matching with the exterior Reissner-Nordstrom metric is achieved. The solution is shown to satisfy the causality criterion 0 < dp/dp < 1 throughout the interior. This solution is studied in detail using the computer package MATHEMATICA (see Mathematica Version 7.0) and shown to possess the necessary qualitative features demanded of such models for physical plausibility, In particular, graphical evidence confirms that the presence of charge has the effect of decreasing the energy density and consequently the radius of the distribution when compared to the Schwarzschild interior. Additionally, we investigate the mass-charge, mass-radius and charge-radius ratios. An explicit barotropic equation of state p = p(p) is obtained for the solution. The solution satisfies the minimum and maximum mass-radius ratios as well as the modified surface redshift upperbound.