Spheres with Two Density Distributions in General Relativity

Abstract

Exact internal solutions have been found in a massive sphere with two different density distributions. The density is a minimum at the surface and increases as we move towards the center; but the density in the the central region is constant at a certain maximum value. The restrictions imposed by pressure-density relations limit the solutions to certain values of $n$ for various ratios of core radius and external radius. $n$ is the parameter expressing the densities in the two regions and the solutions of the field equations.