Relativisitc fluid spheres applicable to neutron star models

A one-parameter family of interior solutions to Einstein's field equations is given. They can be joined continuously to the Schwarzschild exterior, and hence represent fluid spheres of finite radius. Within this family is a set of solutions which represent gaseous spheres defined by the vanishing of the density at the surface. One such solution yields an analytic expression which corresponds to the asymptotic numerical solution of Oppenheimer and Volkoff for the degenerate neutron gas. These gaseous spheres have ratios of specific heats that lie between 1 and 2 in the vicinity of the origin, increasing outward. The sound velocity is less than that of light throughout. These solutions may be applicable in the investigation of stellar interiors where high densities and pressures are of interest. Several previously known solutions are contained within this family