Ideal points in space-time

Abstract

A prescription is given for attaching to a space-time M , subject only to a causality condition, a collection of additional ‘ideal points’. Some of these represent ‘points at infinity’, others ‘singular points’. In particular, for asymptotically simple space-times, the ideal points can be interpreted as the boundary at conformal infinity. The construction is based entirely on the causal structure of M , and so leads to the introduction of ideal points also in a broad class of causal spaces. It is shown that domains of dependence can be characterized in terms of ideal points, and this makes possible an extension of the domain-of-dependence concept to causal spaces. A suggestion is made for assigning a topology to M together with its ideal points. This specifies some singular-point structure for a wide range of possible space-times.