The space of null geodesics and naked singularities

Abstract

The space of null geodesics, , of a spacetime, is considered, with particular reference to the natural topology and manifold structure introduced by Low, where is a strongly causal spacetime. The topology and geometry of the space of a spacetime are used to study the causal structure of . In particular, the question of whether the topology of is Hausdorff carries information on the global structure of . Low has shown that, if be non-Hausdorff, then must be nakedly singular. The converse fails to hold. In this paper, we first introduce two types of naked singularities called ‘nakedly singular future boundary’ and ‘nakedly singular past boundary’. Then investigate the relationships between the presence of each of these naked singularities in , and failure of the Hausdorff property for .