Analytic evidence for the Gubser-Mitra conjecture

TL;DR

This paper provides the first explicit analytic evidence supporting the Gubser-Mitra conjecture by linking classical Gregory-Laflamme instability with thermodynamic stability in charged black strings.

Contribution

It derives a simple master equation for static perturbations of charged black strings, demonstrating the correlation between potential positivity and thermodynamic stability.

Findings

Potential becomes positive when specific heat is positive.

Bound states are forbidden when the potential is positive.

Analytic evidence supports the Gubser-Mitra conjecture.

Abstract

A simple master equation for the static perturbation of charged black strings is derived while employing the gauge proposed by Kol. As the charge is varied it is found that the potential in the master equation for the perturbations becomes positive exactly when the specific heat turns positive thus forbidding a bound state and the onset of the Gregory-Laflamme instability. It can safely be said that this is the first analytic and explicit evidence for the Gubser-Mitra conjecture, correlating the classical and thermodynamic instabilities of black branes. Possible generalizations of the analysis are also discussed.