Gravitation collapse of spherical symmetry with non-uniform density

Abstract

A star with sufficiently large mass will collapse in its senectitude because of gravitation. Many researchers have tried to describe this collapse process. Investigations have been conducted in the case that the star has spherical symmetry and the initial density is uniform. In this article, the case that the initial density is not uniform will be considered. When the density function is high in the center and decreasing with the radius, the collapse process will be described, and in this case, the singularity will only come out in the center because of collision. If the density is not monotonic and there is a crust with high density around the star, it is proved that the non-central collision singularity may come out either in the Schwarzschild sphere or outside of it, i.e., the naked singularize may come out.