Exact solutions for charged spheres and their stability. II. Anisotropic Fluids

Abstract

We study exact solutions of the Einstein-Maxwell equations for the interior gravitational field of static spherically symmetric charged compact spheres. The spheres consist of an anisotropic fluid with a charge distribution that gives rise to a static radial electric field. The density of the fluid has the form $\rho (r)={\rho }_o+\alpha r^2$ (here ${\rho }_o$ and $\alpha$ are constants) and the total charge $q(r)$ within a sphere of radius $r$ has the form $q=\beta r^3$ (with $\beta$ a constant). We evaluate the critical values of $M/R$ for these spheres as a function of $Q/R$ and compare these values with those given by the Andréasson formula.