Self-gravitating branes of codimension 4 in Lovelock gravity

TL;DR

This paper constructs exact solutions for codimension four branes in Lovelock gravity, showing they are non-singular and have discrete tension spectra, advancing the understanding of higher codimension braneworlds.

Contribution

It introduces a family of exact, non-singular solutions for codimension four branes in Lovelock gravity, highlighting unique tension corrections and discrete tension spectra.

Findings

Solutions are free of singularities, only having removable ones.

Brane tension is affected by induced curvature effects.

Tension values are discrete within a given Lovelock theory.

Abstract

We construct a familly of exact solutions of Lovelock equations describing codimension four branes with discrete symmetry in the transverse space. Unlike what is known from pure Einstein gravity, where such brane solutions of higher codimension are singular, the solutions we find, for the complete Lovelock theory, only present removable singularities. The latter account for a localised tension-like energy-momentum tensor on the brane, in analogy with the case of a codimension two self-gravitating cosmic string in pure Einstein gravity. However, the solutions we discuss present two main distinctive features : the tension of the brane receives corrections from the induced curvature of the brane's worldsheet and, in a given Lovelock theory, the spectrum of possible values of the tension is discrete. These solutions provide a new framework for the study of higher codimension braneworlds.