Enveloping branes and braneworld singularities

TL;DR

This paper investigates the singularity structure of braneworld models with bulk matter, revealing that all flat brane solutions encounter finite distance singularities, and explores methods to avoid these singularities which are ultimately unsuccessful under physical constraints.

Contribution

It applies the method of asymptotic splittings to analyze singularities in braneworlds with bulk fluids, showing that finite distance singularities are unavoidable under realistic conditions.

Findings

All flat brane solutions have finite distance singularities.

Cutting and gluing solutions does not avoid singularities under physical constraints.

Physical conditions exclude regular solutions without singularities.

Abstract

The existence of envelopes is studied for systems of differential equations in connection with the method of asymptotic splittings which allows to determine the singularity structure of the solutions. The result is applied to braneworlds consisting of a 3-brane in a five-dimensional bulk, in the presence of an analog of a bulk perfect fluid parametrizing a generic class of bulk matter. We find that all flat brane solutions suffer from a finite distance singularity contrary to previous claims. We then study the possibility of avoiding finite distance singularities by cutting the bulk and gluing regular solutions at the position of the brane. Further imposing physical conditions such as finite Planck mass on the brane and positive energy conditions on the bulk fluid, excludes however this possibility, as well.