Thermodynamics and Stability of Flat Anti-de Sitter Black Strings

Abstract

We examine the thermodynamics and stability of 5-dimensional flat anti-de Sitter (AdS) black strings, locally asymptotically anti-de Sitter spacetimes whose spatial sections are AdS black holes with Ricci flat horizons. We find that there is a phase transition for the flat AdS black string when the AdS soliton string is chosen as the thermal background. We find that this bulk phase transition corresponds to a 4-dimensional flat AdS black hole to AdS soliton phase transition on the boundary Karch-Randall branes. We compute the possibility of a phase transition from a flat AdS black string to a 5-dimensional AdS soliton and show that, though possible for certain thin black strings, the transition to the AdS soliton string is preferred. In contrast to the case of the Schwarzschild-AdS black string, we find that the specific heat of the flat AdS black string is always positive; hence it is thermodynamically stable. We show numerically that both the flat AdS black string and AdS soliton string are free of a Gregory-Laflamme instability for all values of the mass parameter. Therefore the Gubser-Mitra conjecture holds for these spacetimes.

14 pages, 1 figure

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• Hawking radiation from AdS black holes
• Thermodynamic and dynamical stability of Freund-Rubin compactification
• String or branelike solutions in four-dimensional Einstein gravity in the presence of cosmological constant
• Stability of the warped black string with nontrivial topology in five-dimensional Anti-de Sitter spacetime
• Gravitational Instabilities of Uniform Black Strings in AdS