Physical solutions to general-relativistic fluid spheres

Abstract

A method is developed to find physically valid analytic solutions to the Einstein field equations for a static, spherically symmetric distribution of matter. A generating function can be chosen that satisfies physical constraints, and the metric is obtained by quadratures. Three physically valid solutions within the distribution of matter are given as examples. For one of these solutions it is shown that Schwarzschild's interior solution may be obtained as a special case, but only for a specific choice of a parameter which is prohibited by the physical constraints.