Causal functions in general relativity

Abstract

Using the notion of size or volume of future or past of an event, causal functions are defined on a space-time and their behavior is examined in certain space-time models. These functions are then employed to obtain a unified characterization of causality conditions on a spacetime in terms of their simple functional properties like one-oneness, monotonicity, etc. and limiting behavior of these functions along timelike curves. Causal or ideal points boundary of space-time has also been characterized and classified using these causal functions.