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.
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Gnecchi, A., Toldo, C. First order flow for non-extremal AdS black holes and mass from holographic renormalization. J. High Energ. Phys. 2014, 75 (2014). https://doi.org/10.1007/JHEP10(2014)075
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DOI: https://doi.org/10.1007/JHEP10(2014)075