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.