Charged spheres in general relativity

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Abstract
The coupled Einstein-Maxwell field equations are solved by quadratures for spherically symmetric static systems containing charge. In particular, we show how interior metrics can be derived which reduce to classical solutions for neutral distributions of matter when the charge becomes vanishingly small. A number of simple analytic solutions are expressed in order to indicate how charge can change the overall character of these objects. The stability of charged systems is considered. We find the stability of the Schwarzschild interior solution is enhanced by the inclusion of charge, and that an increase in the charge further reduces the critical radius for which instability sets in. The application of this analysis to the solution of Pant and Sah indicates their model is unstable.