Causality and space-time topology

Abstract

Abstract The condition that no material particle signals can travel faster than the velocity of light fixes the causal structure for Minkowski space-time. In general relativity also, which uses the framework of a general space-time manifold, locally the causality relations are the same as in the Minkowski space-time. However, globally there could be important differences in the causal structure due to a different space-time topology, strong gravitational fields and so on. This causal structure of space-time has been studied in detail, especially in view of the occurrence of space-time singularities in gravitational collapse and cosmology (see for example, Penrose, 1972; Hawking and Ellis, 1973; Geroch, 1970b). The purpose of this chapter is to investigate further this causality structure of space-time and its relationship with the space-time topology. The known results and definitions required for later chapters are also reviewed here and several results are established which are of intrinsic interest for the global aspects of space-times and which emphasize the close interplay between the causal structure and topology.