Constraints on the resolution of spacetime singularities

TL;DR

This paper establishes non-perturbative constraints on spacetime singularities using the generalized second law in holographic models, showing that certain singularities cannot be resolved without violating fundamental principles.

Contribution

It proves the GSL non-perturbatively at the species scale in holographic models, enabling constraints on singularity resolution beyond perturbative regimes.

Findings

Outer-trapped surfaces imply geodesic incompleteness non-perturbatively.

Classical BTZ black hole develops a more severe singularity.

Null singularity on Rindler horizon can be resolved by species-scale effects.

Abstract

What happens at spacetime singularities is poorly understood. The Penrose-Wall singularity theorem constrains possible scenarios, but until recently its key assumption--the generalized second law (GSL)--had only been proven perturbatively, severely limiting this application. We highlight that recent progress enables a proof of the GSL in holographic brane-world models, valid non-perturbatively at the species scale $cG$ (with $c$ the number of matter fields and $G$ Newton's constant). This enables genuine constraints: an outer-trapped surface in the Einstein gravity regime implies geodesic incompleteness non-perturbatively at the species scale. Conversely, any genuine resolution must evade Penrose's criteria. We illustrate both possibilities with explicit examples: the classical BTZ black hole evolves to a more severe singularity, while a null singularity on the Rindler horizon is resolved, both by species-scale effects. Subject to the GSL, these constraints on singularity resolution apply beyond brane-worlds: namely, in any theory with a geometric UV scale--roughly, where the metric remains well-defined but classical Einstein gravity breaks down.