Curved branes with regular support

TL;DR

This paper investigates singularities in five-dimensional curved brane models, demonstrating that curved branes can have singularity-free solutions under certain conditions, unlike flat branes which always exhibit singularities.

Contribution

It introduces a new analysis of spacetime singularities in curved branes within braneworld models, showing the possibility of regular solutions with specific equations of state.

Findings

Flat branes always have finite distance singularities.

Curved branes can have singularity-free solutions.

Solutions are compatible with the null energy condition.

Abstract

We study spacetime singularities in a general five-dimensional braneworld with curved branes satisfying four-dimensional maximal symmetry. The bulk is supported by an analog of perfect fluid with the time replaced by the extra coordinate. We show that contrary to the existence of finite distance singularities from the brane location in any solution with flat (Minkowski) branes, in the case of curved branes there are singularity-free solutions for a range of equations of state compatible with the null energy condition.