On Black-Brane Instability In an Arbitrary Dimension

Details On Black-Brane Instability In an Arbitrary Dimension On Black-Brane Instability In an Arbitrary Dimension

2004-07-15

arxiv.org/abs/gr-qc/0407058v2

Class.Quant.Grav.21:4793-4804,2004

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

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

Scientific paper

10.1088/0264-9381/21/21/003

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 $D\leq 11$.

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