Analytic evidence for 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.

Magnetic charge can locally stabilize Kaluza–Klein bubbles

“…Perturbative stability,à la Gregory-Laflamme, of black strings with magnetic charge and mass parameters P and m, consistent with the notation in this letter, was demonstrated to hold in the range P ≤ m ≤ 3 2 √ 2 P , corresponding to where the heat capacity is positive [7]. While this was regarded as evidence that the Gubser-Mitra conjecture is satisfied for these objects, a proper thermodynamic stability analysis was not possible since it was unclear what the magnetic black string could phase transition to.…”

Quantum quench in matrix models: dynamical phase transitions, selective equilibration and the Generalized Gibbs Ensemble

“…8 (a); now as we decrease L, the dual circle L ′ starts to increase and the uniformly smeared D1 soliton starts getting stretched and as L ′ increases beyond a certain critical size, it becomes unstable towards breaking and forming a localized soliton. In [58], Gregory and Laflamme predicted such a transition as a thermodynamic phase transition [59,60,61,62]. Thus, the dynamical gapless → gapped transition in our model translates to a dynamical GL transition from a uniform to a localized soliton.…”

Blackfolds in supergravity and string theory

“…The disappearance of the marginally unstable GL zero-mode when (4.5) is satisfied has been verified explicitly for several classes of charged black branes in [19,20,21,22,23,24,25]. However, it is important to realize that here we are not (yet) describing these zero modes of finite wavelength, but rather identifying an instability of hydrodynamic modes, with small frequency at very long wavelengths.…”

“…Numerical results for the threshold mode of several black branes have been computed in [19,21,22,23,24,25]. While we have not performed a detailed comparison, plots of k| thr as a function of the charge appear to show good qualitative agreement with (4.10).…”

“…In the case of non-dilatonic branes, refs. [22,24,25] have observed that near the critical value of the charge Q crit p at which c 2 s = 0, the threshold mode behaves like 6…”