Spheres with Two Density Distributions in General Relativity

Exact internal solutions have been found for a massive sphere with two different density distributions. The density has its minimum at the surface, and it increases inversely as the square of the distance as we move towards the center. There is a core of constant density ${\rho }_c$ and radius $r=b$. The restrictions imposed by pressure and density relations limit the solutions to certain values of $n$, the parameter which determines the Schwarzschild ratio of the sphere.