K-Causal Structure of Space-Time in General Relativity

TL;DR

This paper generalizes causal structures in space-time using K-causality, introduces new causality conditions, and demonstrates their relationships, providing a simpler, more general framework applicable to various physical and mathematical scenarios.

Contribution

It extends the theory of causal maps with K-causality, introduces new causality conditions, and relates them to classical causality concepts, simplifying the analysis of space-time structures.

Findings

Introduced a new causality condition between global hyperbolicity and causal simplicity.

Proved relationships among various causality conditions in K-causality framework.

Applied the approach to space-time structures with singularities and topology change.

Abstract

Using K-causal relation introduced by Sorkin and Woolgar [26], we gener- alize results of Garcia-Parrado and Senovilla [8, 9] on causal maps. We also introduce causality conditions with respect to K-causality which are analogous to those in classical causality theory and prove their inter relationships. We introduce a new causality condition following the work of Bombelli and Noldus [3] and show that this condition lies in between global hyperbolicity and causal simplicity. This approach is simpler and more general as compared to traditional causal approach [11, 19] and it has been used by Penrose et.al [20] in giving a new proof of positivity of mass theorem. C^0 space-time structures arise in many mathematical and physical situations like conical singularities, discontinuous matter distributions, phenomena of topology-change in quantum field theory etc.