Causal boundary for strongly causal spacetimes

Abstract

A study of the general framework for the causal boundary is presented, and for various separation properties necessary and sufficient conditions are proved. As a consequence, it is shown that the usual implicit topological identification rule, imposed on the 'preboundary' of the spacetime to obtain the right boundary structure, might in general not exist. To rule out this difficulty, a new explicit identification rule is proposed. This new identification seems to yield the intuitively expected point set structure of the boundary, onto which the chronology relation can be extended.