On Black-Brane Instability In an Arbitrary Dimension

TL;DR

This paper investigates the stability of black branes across various spacetime dimensions, deriving large D asymptotics and explicit critical mass expressions for different compactification manifolds, highlighting potential phase transition changes.

Contribution

It provides the first large D asymptotic analysis of black-brane stability and explicit formulas for critical mass on arbitrary compactification manifolds, including higher-dimensional tori.

Findings

Critical dimension for phase transition change could be as low as D ≤ 11.

Derived explicit critical mass formulas for black branes on tori.

Large D asymptotics of marginally stable black strings obtained.

Abstract

The black-hole black-string system is known to exhibit critical dimensions and therefore it is interesting to vary the spacetime dimension $D$, treating it as a parameter of the system. We derive the large $D$ asymptotics of the critical, i.e. marginally stable, string following an earlier numerical analysis. For a background with an arbitrary compactification manifold we give an expression for the critical mass of a corresponding black brane. This expression is completely explicit for ${\bf T}^n$, the $n$ dimensional torus of an arbitrary shape. An indication is given that by employing a higher dimensional torus, rather than a single compact dimension, the total critical dimension above which the nature of the black-brane black-hole phase transition changes from sudden to smooth could be as low as $D\leq 11$.