Exact solutions for charged spheres and their stability. I. Perfect Fluids

We study exact solutions of the Einstein-Maxwell equations for the interior gravitational field of static spherically symmetric charged compact spheres. The spheres are composed of a perfect fluid with a charge distribution that creates a static radial electric field. The inertial mass density of the fluid has the form $ρ(r) = ρ_o + αr^2$ ($ρ_o$ and $α$ are constants) and the total charge $q(r)$ within a sphere of radius $r$ has the form $q = βr^3$ ($β$ is 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.

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