Optical scalars and singularity avoidance in spherical spacetimes

Abstract

Consider a spherically symmetric spacelike slice through a spacetime. One can derive universal bounds on any such slice assuming that the matter sources satisfy an energy condition and that the slice be regular. These bounds are used to derive the horizon formation conditions and to show how a regular spacelike slicing may avoid singularities. The results hold true even when the matter has a distribution on a shell or blows up at the origin so as to give a conical singularity.