Spheres with varying density in general relativity

Abstract

Exact internal solutions for massive spheres with three different distributions of density have been found. The central core density is considered to be constant while the outer region has two types of varying densities: (i) varying inversely as the square of the radial distance; (ii) varying parabolically as rho varies as 1-r2/constant. The solutions are found to be continuous at different boundaries while the densities of different regions are not continuous but vary slightly. With proper choice of different parameters appearing in the solutions, the results can be applied to actual problems of stellar physics.