Brane singularities with a scalar field bulk

TL;DR

This paper analyzes the singularity structure of a 3-brane with a scalar field in five dimensions, showing that avoiding collapse singularities requires the brane to have non-zero curvature.

Contribution

It provides a general analysis of brane singularities with scalar fields using asymptotic splittings, revealing conditions to avoid collapse singularities.

Findings

Collapse singularity can be avoided only with curved branes

Singularity structure depends on brane curvature

Asymptotic analysis clarifies conditions for regularity

Abstract

The singularity structure and the corresponding asymptotic behavior of a 3-brane coupled to a scalar field in a five dimensional bulk is analyzed in full generality, using the method of asymptotic splittings. It is shown that the collapse singularity at a finite distance from the brane can be avoided only at the expense of making the brane world-volume positively or negatively curved.