K-causal Structure of Space-time in General Relativity

Using K-causal relation introduced by Sorkin and Woolgar [26], we generalize 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. C0 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.