Abstract
We study the thermodynamics of $AdS_4$ black hole solutions of Einstein-Maxwell theory that are accelerating, rotating, and carry electric and magnetic charges. We focus on the class for which the black hole horizon is a spindle and can be uplifted on regular Sasaki-Einstein spaces to give solutions of $D=11$ supergravity that are free from conical singularities. We use holography to calculate the Euclidean on-shell action and to define a set of conserved charges which give rise to a first law. We identify a complex locus of supersymmetric and non-extremal solutions, defined through an analytic continuation of the parameters, upon which we obtain a simple expression for the on-shell action. A Legendre transform of this action combined with a reality constraint then leads to the Bekenstein-Hawking entropy for the class of supersymmetric and extremal black holes.
Highlights
The study of black hole thermodynamics in the context of the AdS=CFT correspondence continues to be a very active area of research
We study the thermodynamics of AdS4 black hole solutions of Einstein-Maxwell theory that are accelerating, rotating, and carry electric and magnetic charges
We focus on the class for which the black hole horizon is a spindle and can be uplifted on regular Sasaki-Einstein spaces to give solutions of D 1⁄4 11 supergravity that are free from conical singularities
Summary
The study of black hole thermodynamics in the context of the AdS=CFT correspondence continues to be a very active area of research. The regular, supersymmetric and extremal accelerating black holes are specified by a single parameter which can be taken to be the electric charge Qe. The angular momentum J and Bekenstein-Hawking entropy, SBH, are given by [25], Qe 4. Motivated by recent progress for the Kerr-Newman and other black holes [3,23], we can develop an analogous prescription for supersymmetric and extremal black holes To do this we first introduce a complex locus of supersymmetric solutions that is obtained by an analytic continuation of some of the parameters appearing in the black hole solutions. By analyzing various thermodynamic quantities, analytically continued to this complex locus, we are able to derive an expression for the on-shell Euclidean action I 1⁄4 Iðω; φÞ, expressed as a function of rotational and electric chemical potentials, ω and φ, respectively, both of which are complex and defined on the supersymmetric locus. In the Appendix we show that for supersymmetric solutions, the boundary metric and gauge field can be recast in a canonical form as studied in [37]
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