Exploding spheres of dust

In this paper, we extend the work of Oppenheimer & Snyder (1939) who treated the zero curvature case in the gravitational collapse of spheres of dust intended to represent collapsing stars. A solution is given which is valid for all space and is characterized by negative curvature of the space within a sphere of dust. This solution is obtained by matching the negative curvature interior solution (as well as, for completeness, zero and positive curvatures interior solutions) to an exterior Schwarzschild geometry. In this solution, corresponding to the case of a Newtonian system with positive total energy, the mass as seen by an observer at infinity is found to be positive definite. Also, in each case, the positive definite massm is related to the density and radiusr defined as the square root of the (surface area/4)] of the dust cloud viam=(4/3)pr ³. The methods employed here for matching interior and exterior solutions are applicable to the construction of cosmological models in which the sign of the curvature and/or expansion rate differ in two or more regions, e.g. a universe expanding in one region and contracting in another.