Thermodynamics and Stability of Flat Anti-de Sitter Black Strings

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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.