Exact Solutions for Oscillating Spheres in General Relativity

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Abstract
A class of exact interior solutions is given for adiabatic spherically symmetric motion of a perfect fluid of uniform density but non-uniform pressure. This is matched to the Schwarzschild exterior solution at a moving boundary. The solutions include cases of oscillating motion in which both the pressure and the density are always positive, and the metric non-singular. Such cases are possible models for quasar oscillations, provided it is permissible to ignore radiation flux; the period is calculated in an example. The Schwarzschild static interior solution is shown to be stable to perturbations in which the density remains uniform, provided the ratio mass/radius is not too great.

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