Perturbations of Black p-Branes

TL;DR

This paper analyzes scalar and tensorial perturbations of black p-branes, finding no instabilities and providing insights into their stability and implications for the AdS/CFT correspondence.

Contribution

It derives and compares scalar and tensor perturbation equations for black p-branes, confirming their stability and exploring implications for gauge/gravity duality.

Findings

No instabilities found in perturbations.

Scalar and tensor perturbations yield consistent results.

Supports the stability of black p-branes in string theory.

Abstract

We consider black $p$-brane solutions of the low energy string action, computing scalar perturbations. Using standard methods, we derive the wave equations obeyed by the perturbations and treat them analytically and numerically. We have found that tensorial perturbations obtained via a gauge-invariant formalism leads to the same results as scalar perturbations. No instability has been found. Asymptotically, these solutions typically reduce to a $AdS_{(p+2)}\times S^{(8-p)}$ space, which, in the framework of Maldacena's conjecture, can be regarded as a gravitational dual to a conformal field theory defined in a $(p+1)$-dimensional flat space-time. The results presented open the possibility of a better understanding the AdS/CFT correspondence, as originally formulated in terms of the relation among brane structures and gauge theories.