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Register a new userMicroscopic origin of the Bekenstein-Hawking entropy of supersymmetric AdS$_{bf 5}$ black holes
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We present a holographic derivation of the entropy of supersymmetric asymptotically AdS$_5$ black holes. We define a BPS limit of black hole thermodynamics by first focussing on a supersymmetric family of complexified solutions and then reaching extremality. We show that in this limit the black hole entropy is the Legendre transform of the on-shell gravitational action with respect to three chemical potentials subject to a constraint. This constraint follows from supersymmetry and regularity in the Euclidean bulk geometry. Further, we calculate, using localization, the exact partition function of the dual $mathcal{N}=1$ SCFT on a twisted $S^1times S^3$ with complexified chemical potentials obeying this constraint. This defines a generalization of the supersymmetric Casimir energy, whose Legendre transform at large $N$ exactly reproduces the Bekenstein-Hawking entropy of the black hole.
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Vacuum Einstein equations when projected on to a black hole horizon is analogous to the dynamics of fluids. In this work we address the question, whether certain properties of semi-classical black holes could be holographically mapped into properties of (2 + 1)-dimensional fluid living on the horizon. In particular, we focus on the statistical mechanical description of the horizon-fluid that leads to Bekenstein-Hawking entropy. Within the paradigm of Landau mean field theory and existence of a condensate at a critical temperature, we explicitly show that Bekenstein-Hawking entropy and other features of black hole thermodynamics can be recovered from the statistical modelling of the fluid. We also show that a negative cosmological constant acts like an external magnetic field that induces order in the system leading to the appearance of a tri-critical point in the phase diagram.
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We present new analytic rotating AdS$_4$ black holes, found as solutions of 4d gauged $mathcal{N}=2$ supergravity coupled to abelian vector multiplets with a symmetric scalar manifold. These configurations preserve two real supercharges and have a smooth limit to the BPS Kerr-Newman-AdS$_4$ black hole. We spell out the solution of the $STU$ model admitting an uplift to M-theory on S$^7$. We identify an entropy function, which upon extremization gives the black hole entropy, to be holographically reproduced by the leading $N$ contribution of the generalized superconformal index of the dual theory.
In arbitrary dimension, we consider a theory described by the most general quadratic curvature corrections of Einstein gravity together with a self-interacting nonminimally coupled scalar field. This theory is shown to admit five different families of Lifshitz black holes dressed with a nontrivial scalar field. The entropy of these configurations is microscopically computed by means of a higher-dimensional anisotropic Cardy-like formula where the role of the ground state is played by the soliton obtained through a double analytic continuation. This involves to calculate the correct expressions for the masses of the higher-dimensional Lifshitz black hole as well as their corresponding soliton. The robustness of this Cardy-like formula is checked by showing that the microscopic entropy is in perfect agreement with the gravitational Wald entropy. Consequently, the calculated global charges are compatible with the first law of thermodynamics. We also verify that all the configurations satisfy an anisotropic higher-dimensional version of the Smarr formula.
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