K-Causal Structure of Space-Time in General Relativity

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.

16 pages, 4 figures

References in corpus (4)

• A domain of spacetime intervals in general relativity
• The moduli space of isometry classes of globally hyperbolic spacetimes
• General study and basic properties of causal symmetries
• Compactness of the space of causal curves

Cited by in corpus (2)

• K-causality coincides with stable causality
• Causal Cones, Cone Preserving Transformations and Causal Structure in Special and General Theory of Relativity