K-causal structure of space-time in general

relativity

SUJATHA JANARDHAN^1,* and R V SARAYKAR²

¹Department of Mathematics, St. Francis De Sales College, Nagpur 440 006, India

²Department of Mathematics, R.T.M. Nagpur University, Nagpur 440 033, India

^*Corresponding author

E-mail: sujata\_jana@yahoo.com; r\_saraykar@rediffmail.com

Abstract. Using K-causal relation

introduced by Sorkin and Woolgar [1], we generalize results of

Garcia-Parrado and Senovilla [2,3] 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 [4] 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 [5,6] and it has been used by

Penrose {\it et al} [7] 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.

Keywords. $C^{0}$-space-times; causal maps; causality conditions; K-causality.

PACS Nos 04.20.-q; 02.40.Pc