Spacetime singularities as sources of a conserved gravitational flux

Abstract

Spacetime singularities are regarded as sources or sinks of a conserved gravitational flux. The flux lines are viewed as curves belonging, not to the spacetime manifold M, but to the tangent fibre bundle over M. These lines are determined by timelike and null geodesics referred to a suitable nonaffine parameter. With the help of this approach to the study of singularities a simple proof is given of Penrose's theorem on the occurrence of a singularity in a star undergoing asymmetric gravitational collapse.