Universality classes for horizon instabilities

TL;DR

The paper develops a universality-class framework for horizon instabilities (Gregory-Laflamme) in the supergravity regime, identifying that non-dilatonic D3, M2, and M5 branes share a crossover from instability to stability at a specific non-extremal mass and that the shortest unstable wavelength diverges with a common critical exponent. By reducing gravity with scalars to a 2+1D effective theory and focusing on near-horizon Chamblin-Reall scaling, the authors classify stability through a single exponent $\gamma$ and tie thermodynamic scaling $S \propto V T^{\alpha}$, with $\alpha = \frac{D-2}{1 - 2 \gamma^2 (D-2)}$, to dynamical stability. Static threshold perturbations are used to diagnose the onset of instability, and numerical analysis shows the threshold wavenumber $k$ vanishes near the stability boundary as $k \sim \sqrt{\gamma - \gamma^*}$ (or equivalently in terms of horizon parameters), supporting the proposed universality across D3, M2, and M5 branes. The results reinforce the link between thermodynamics and dynamical stability and provide a unified description of horizon instabilities with potential implications for holography and the end states of GL dynamics.

Abstract

We introduce a notion of universality classes for the Gregory-Laflamme instability and determine, in the supergravity approximation, the stability of a variety of solutions, including the non-extremal D3-brane, M2-brane, and M5-brane. These three non-dilatonic branes cross over from instability to stability at a certain non-extremal mass. Numerical analysis suggests that the wavelength of the shortest unstable mode diverges as one approaches the cross-over point from above, with a simple critical exponent which is the same in all three cases.

Figures (2)

• Figure 1: Stability of Chamblin-Reall solutions. The dots represent threshold instabilities of the Chamblin-Reall solutions. The vertical line at $\gamma^*=1/\sqrt{2}$ indicates the thermodynamic stability limit.
• Figure 2: Instabilities of black D3, M2, and M5-branes. The dots represent threshold instabilities of the black branes we found. The vertical lines indicate the thermodynamic stability limits, which were found by (\ref{['rzeroStr']}), with $\tilde{R}=1$ for the D3-brane, $\tilde{R}=(1/3)^{1/6}$ for the M2-brane, and $\tilde{R}=(2/3)^{1/3}$ for the M5-brane. The curves indicate wavenumbers of threshold instabilities of uncharged black branes, with $r_0$ being the Schwarzchild radius.