Causality violations and singularities

Abstract

We announce and justify two theorems (proofs will appear in Refs. 1 and 2): i) A generalization of the singularity theorem of Hawking and Penrose [3] to space-times with chronology violations. Although it is impossible to remove the chronology condition completely the announced theorem is in a well defined sense optimal: the chronology condition is replaced by a strictly weaker condition that cannot be removed because of counter examples, ii) If the chronology violating setV has compact closure and the strong energy and generic conditions hold, thenV is generated by incomplete null geodesics. It follows that if the region of causality violation does not extend to infinity thenV contains singularities.