Singularities From Entropy

TL;DR

This paper proves a new singularity theorem based on entropy bounds, linking quantum information to spacetime singularities, applicable even in closed universes and involving hyperentropic regions.

Contribution

It introduces a singularity theorem derived from the Bousso bound, connecting entropy conditions with geodesic incompleteness, extending Penrose's theorem to hyperentropic contexts.

Findings

Hyperentropic regions imply geodesic incompleteness under contracting light rays.

The theorem applies to closed universes and asymptotically de Sitter spacetimes.

Soft radiation can recover Penrose's theorem in flat space.

Abstract

Assuming the Bousso bound, we prove a singularity theorem: if the light rays entering a hyperentropic region contract, then at least one light ray must be incomplete. "Hyperentropic" means that the entropy of the region exceeds the Bekenstein-Hawking entropy of its spatial boundary. Our theorem provides a direct link between singularities and quantum information. The hyperentropic condition replaces the noncompactness assumption in Penrose's theorem, so our theorem is applicable even in a closed universe. In an asymptotically de Sitter spacetime, for example, a big bang singularity can be diagnosed from the presence of dilute radiation at arbitrarily late times. In asymptotically flat space, Penrose's theorem can be recovered by adding soft radiation.