Analytic evidence for the Gubser-Mitra conjecture

A simple master equation for the static perturbation of charged black strings is derived with employing the gauge proposed by Kol. The sign changes of the potential in the master equation and specific heat of the background exactly coincide. That is, for the black strings with positive specific heat, the potential becomes positive definite to forbid the bound state implying the onset of 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.