Universality classes for horizon instabilities

TL;DR

This paper introduces universality classes for horizon instabilities, analyzing the stability of various supergravity solutions and revealing a common critical behavior near stability transitions.

Contribution

It defines universality classes for Gregory-Laflamme instabilities and analyzes the stability of non-extremal branes within supergravity, identifying a shared critical exponent.

Findings

Non-extremal D3, M2, M5-branes exhibit a crossover from instability to stability.

The shortest unstable mode wavelength diverges at the stability transition.

A universal critical exponent characterizes the divergence across different branes.

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.