Physical solutions to general-relativistic fluid spheres.

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 such that it satisfies physical constraints, and the metric is obtained by quadratures. Three physically valid solutions (i.e., infinity>..mu..>p>0, p'>0, dp/d..mu..<1 within the distribution of matter, where ..mu.. and p are the density and pressure, respectively) 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 (d..mu../dp=0 in Schwarzschild's interior solution).