Hawking-Type Singularity Theorems for Worldvolume Energy Inequalities

Abstract

The classical singularity theorems of R. Penrose and S. Hawking from the 1960s show that, given a pointwise energy condition (and some causality as well as initial assumptions), spacetimes cannot be geodesically complete. Despite their great success, the theorems leave room for physically relevant improvements, especially regarding the classical energy conditions as essentially any quantum field theory necessarily violates them. While singularity theorems with weakened energy conditions exist for worldline integral bounds, so-called worldvolume bounds are in some cases more applicable than the worldline ones, such as the case of some massive free fields. In this paper, we study integral Ricci curvature bounds based on worldvolume quantum strong energy inequalities. Under the additional assumption of a—potentially very negative—global timelike Ricci curvature bound, a Hawking-type singularity theorem is proved. Finally, we apply the theorem to a cosmological scenario proving past geodesic incompleteness in cases where the worldline theorem was inconclusive.