First order flow for non-extremal AdS black holes and mass from holographic renormalization

Abstract

In this paper we present a first order formulation for non-extremal Anti-de Sitter black hole solutions in four dimensional $\mathcal{N}=2$ U(1)-gauged Supergravity. The dynamics is determined in terms of a quantity $\mathcal{W}$ which plays the role of a superpotential for the gauging potential in the action. We show how the first order flow arises from writing the action as a sum of squares and we identify the superpotential driving the first order flow for two classes of solutions (electric and magnetic) of the $t^3$ model. After identifying $\mathcal{W}$, we study the Hamilton-Jacobi holographic renormalization procedure in presence of mixed boundary conditions for the scalar fields. We compute the renormalized on-shell action and the mass of the black hole configurations. The expression obtained for the mass satisfies the first law of thermodynamics.

36 pages, v3: renormalized free energy expression corrected, comparison of the on-shell action between electric and magnetic solution added

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• Black holes with halos
• Quarter-BPS Black Holes in AdS${}_4$-NUT from $N=2$ Gauged Supergravity
• First order flow equations for nonextremal black holes in AdS (super)gravity
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• Thermodynamics of spinning AdS4 black holes in gauged supergravity
• Holography of AdS Hairy Black Holes and Cardy-Verlinde Formula
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