On Black-Brane Instability In an Arbitrary Dimension

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 ${\mathbf{T}}^n$, 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 $D\le 11$.

1+14 pages, 2 eps figures. Replaced with the published version

References in corpus (2)

• A Dialogue of Multipoles: Matched Asymptotic Expansion for Caged Black Holes
• Sequences of Bubbles and Holes: New Phases of Kaluza-Klein Black Holes

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