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 thermodynamic stability implies perturbative stability for this spacetime. This may indicate that a generalization of the Gubser-Mitra conjecture, in which the assumption of a translational killing vector is weakened to that of a conformal killing vector of translational form, holds under certain conditions.