A criterion for admissible singularities in brane world

TL;DR

This paper proposes a criterion for determining the physical admissibility of singularities in brane world models with gravity and scalar fields in Anti-de Sitter space, linking it to Gubser's bounded potential conjecture.

Contribution

It introduces a new criterion based on the finiteness of the on-shell Lagrangian integral, which aligns with Gubser's conjecture about potential bounds, explaining its validity.

Findings

The criterion matches Gubser's bounded potential condition.

It applies to various classes of singularities in the studied models.

Provides a physical basis for the admissibility of singularities.

Abstract

When gravity couples to scalar fields in Anti-de Sitter space, the geometry becomes non-AdS and develops singularities generally. We propose a criterion that the singularity is physically admissible if the integral of the on-shell Lagrangian density over the finite range is finite everywhere. For all classes of the singularities studied here, the criterion suggested in this paper coincides with an independent proposal made by Gubser that the potential should be bounded from above in the solution. This gives a reason why Gubser's conjecture works.