Universality classes for horizon instabilities

Abstract

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.

Smeared branes and the Gubser-Mitra conjecture

“…This result should be contrasted with the analysis of p-brane solutions in [8,9,10]. In those studies, it was found that for the ten-dimensional supergravity p-brane solutions with p ≤ 4, there is a threshold unstable mode for the neutral case, but this mode goes off to infinite wavelength at a critical value of the charge, signalling the disappearance of the instability.…”

“…This is a natural extension of the investigation of p-branes in [6,8,9,10]. The two classes of solutions are related by T-duality, which implies that the thermodynamics of the smeared branes is identical to that of the p-brane with the same total number of extended directions.…”

“…However, following [6,8,9], we will assume that there is no charged field in the theory, so the charge is not allowed to vary, and focus on the specific heat: we take the condition for thermodynamic stability to be the positivity of the specific heat,…”

“…In appendix A, we discuss the extent to which this argument can be generalised to the charged case. The important point for our present purpose is that this implies that any solution of the equations of motion describing a neutral black string, uniform or non-uniform, can be written in the form (9). This provides a convenient framework for discussing solutions.…”

The Gregory-Laflamme instability for the D2–D0 bound state

“…A reason to be particularly interested in the GL instability for the near -extremal D2-D0 bound state is that it interpolates between near -extremal D2-branes, for which it is known there is no instability [5] and near-extremal smeared D0-branes, for which it has been argued that there is a GL instability [6,7,8]. The interpolation itself is interesting: the dynamics of the bound state has been argued to correspond to non-commutative field theory (NCFT) [9].…”