Singularities and causality violation

Abstract

Abstract A number of important theorems in General Relativity have required a causality assumption; for example, the Geroch topology change theorem, and most of the Hawking-Penrose-Geroch singularity theorems. It is shown in this paper that the causality condition can be replaced by weaker causality conditions, and in some cases removed altogether. In particular, (a) it is shown that if the Einstein equations (and the weak energy condition) hold on the “topology-changing” space-time considered by Geroch, then topology change cannot occur. No causality assumption is needed in the proof. Furthermore, it is shown that if topology change occurs within a finite region, then this change of topology must be accompanied by singularities. (b) It is shown that causality violation cannot prevent the Hawking-Penrose-Geroch singularities unless the causality violation begins “at infinity”—a region which is free of matter and gravitational radiation—and this seems very unlikely.