The light-cone theorem

TL;DR

This paper proves a geometric inequality relating the area of light-cone cross-sections in certain space-times to those in standard models, with equality characterizing the exact model space-time.

Contribution

It establishes a new light-cone area inequality under energy conditions, characterizing when equality occurs in terms of the space-time metric.

Findings

Area of light-cone cross-sections is bounded by model space-times.

Equality holds only for the exact model space-time.

Results apply to space-times satisfying specific energy conditions.

Abstract

We prove that the area of cross-sections of light-cones, in space-times satisfying suitable energy conditions, is smaller than or equal to that of the corresponding cross-sections in Minkowski, or de Sitter, or anti-de Sitter space-time. The equality holds if and only if the metric coincides with the corresponding model in the domain of dependence of the light-cone.