Geometry of deformations of branes in warped backgrounds

TL;DR

This paper investigates the geometric conditions for stable, extremal branes in warped backgrounds, deriving stability criteria and analyzing deformations, with applications to various braneworld models and generalizations.

Contribution

It provides a geometric framework for analyzing brane stability in warped spacetimes, including new stability conditions and extensions to curved and higher co-dimension branes.

Findings

Warp factor must have a minimum at the brane for stability.

Derived Jacobi equations for normal deformations.

Verified criteria on known braneworld models.

Abstract

The `braneworld' (described by the usual worldvolume action) is a D dimensional timelike surface embedded in a N dimensional ($N>D$) warped, nonfactorisable spacetime. We first address the conditions on the warp factor required to have an extremal flat brane in a five dimensional background. Subsequently, we deal with normal deformations of such extremal branes. The ensuing Jacobi equations are analysed to obtain the stability condition. It turns out that to have a stable brane, the warp factor should have a minimum at the location of the brane in the given background spacetime. To illustrate our results we explicitly check the extremality and stability criteria for a few known co-dimension one braneworld models. Generalisations of the above formalism for the cases of (i) curved branes (ii) asymmetrical warping and (iii) higher co-dimension braneworlds are then presented alongwith some typical examples for each. Finally, we summarize our results and provide perspectives for future work along these lines.