Volume Singularities in General Relativity

TL;DR

This paper introduces a new type of singularity in General Relativity called volume singularities, characterized by regions with arbitrarily small spacetime volume, and explores their implications in cosmology and black hole physics.

Contribution

It defines volume singularities as a complement to traditional singularity notions and analyzes their occurrence and implications in cosmological and black hole scenarios.

Findings

Geodesic singularities are also volume singularities in cosmology.

Volume singularities are always hidden behind event horizons in black holes.

The concept supports discussions on cosmic censorship conjecture.

Abstract

We propose a new notion of singularity in General Relativity which complements the usual notions of geodesic incompleteness and curvature singularities. Concretely, we say that a spacetime has a volume singularity if there exist points whose future or past has arbitrarily small spacetime volume: in particular, smaller than a Planck volume. From a cosmological perspective, we show that the (geodesic) singularities predicted by Hawking's theorem are also volume singularities. In the black hole setting, we show that volume singularities are always hidden by an event horizon, prompting a discussion of Penrose's cosmic censorship conjecture.