Thermodynamics of third order Lovelock anti-de Sitter black holes revisited

Abstract

We compute the mass and the temperature of third order Lovelock black holes with negative Gauss-Bonnet coefficient ${\alpha }_2<0$ in anti-de Sitter space and perform the stability analysis of topological black holes. When $k=-1$, the third order Lovelock black holes are thermodynamically stable for the whole range $r_{+}$. When $k=1$, we found that the black hole has an intermediate unstable phase for $D=7$. In eight dimensional spacetimes, however, a new phase of thermodynamically unstable small black holes appears if the coefficient $\tilde{\alpha }$ is under a critical value. For $D\ge 9$, black holes have similar the distributions of thermodynamically stable regions to the case where the coefficient $\tilde{\alpha }$ is under a critical value for $D=8$. It is worth to mention that all the thermodynamic and conserved quantities of the black holes with flat horizon don't depend on the Lovelock coefficients and are the same as those of black holes in general gravity.

arXiv comment15 pages, 22 figures

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• Thermodynamics of Third Order Lovelock-Born-Infeld Black Holes
• Thermodynamic phase transition rate for the third-order Lovelock black hole in diverse dimensions
• A Universal Lower Bound on the Specific Temperatures of AdS-Reissner-Nordstrom Black Holes with Flat Event Horizons
• Black hole solution in third order Lovelock gravity has no Gauss-Bonnet limit
• Non-extended phase space thermodynamics of Lovelock AdS black holes in grand canonical ensemble
• Thermodynamic phase transition and winding number for the third-order Lovelock black hole
• Inhomogeneous metrics on complex bundles in Lovelock gravity
• A new metric for rotating charged Gauss-Bonnet black holes in AdS spaces
• Holographic dark energy satisfying the energy conditions in Lovelock gravity
• The constraint equations of Lovelock gravity theories: a new ${\sigma }_k$-Yamabe problem