Naked shell singularities on the brane

TL;DR

This paper constructs static, spherically symmetric braneworld models with naked shell singularities using non-standard slicings of 5D Schwarzschild spacetimes, revealing exotic matter and potential quantum corrections.

Contribution

It introduces a novel method of generating braneworld solutions with naked singularities via isotropic coordinate slicings, highlighting their physical and holographic implications.

Findings

Brane matter behaves as a perfect fluid with an exotic equation of state.

Singular horizons are associated with pressure singularities at the brane crossing the bulk horizon.

Exotic matter distributions and singular horizons are common in generalized slicings of Ricci-flat bulks.

Abstract

By utilizing non-standard slicings of 5-dimensional Schwarzschild and Schwarzschild-AdS manifolds based on isotropic coordinates, we generate static and spherically symmetric braneworld spacetimes containing shell-like naked null singularities. For planar slicings, we find that the brane-matter sourcing the solution is a perfect fluid with an exotic equation of state and a pressure singularity where the brane crosses the bulk horizon. From a relativistic point of view, such a singularity is required to maintain matter infinitesimally above the surface of a black hole. From the point of view of the AdS/CFT conjecture, the singular horizon can be seen as one possible quantum correction to a classical black hole geometry. Various generalizations of planar slicings are also considered for a Ricci-flat bulk, and we find that singular horizons and exotic matter distributions are common features.