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Register a new userCFT Duals for Accelerating Black Holes
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Authors
Marco Astorino
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The near horizon geometry of the rotating C-metric, describing accelerating Kerr-Newman black holes, is analysed. It is shown that, at extremality, even though not it is isomorphic to the extremal Kerr-Newman, it remains a warped and twisted product of $AdS_2 times S^2$. Therefore the methods of the Kerr/CFT correspondence can successfully be applied to build a CFT dual model, whose entropy reproduce, through the Cardy formula, the Beckenstein-Hawking entropy of the accelerating black hole. The mass of accelerating Kerr-Newman black hole, which fulfil the first law of thermodynamics, is presented. Further generalisation in presence of an external Melvin-like magnetic field, used to regularise the conical singularity characteristic of the C-metrics, shows that the Kerr/CFT correspondence can be applied also for the accelerating and magnetised extremal black holes.
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Kerr/CFT correspondence has been recently applied to various types of 5D extremal rotating black holes. A common feature of all such examples is the existence of two chiral CFT duals corresponding to the U(1) symmetries of the near horizon geometry. In this paper, by studying the moduli space of the near horizon metric of five dimensional extremal black holes which are asymptotically flat or AdS, we realize an SL(2,Z) modular group which is a symmetry of the near horizon geometry. We show that there is a lattice of chiral CFT duals corresponding to the moduli points identified under the action of the modular group. The microscopic entropy corresponding to all such CFTs are equivalent and are in agreement with the Bekenstein-Hawking entropy.
We study solutions in the Plebanski--Demianski family which describe an accelerating, rotating and dyonically charged black hole in $AdS_4$. These are solutions of $D=4$ Einstein-Maxwell theory with a negative cosmological constant and hence minimal $D=4$ gauged supergravity. It is well known that when the acceleration is non-vanishing the $D=4$ black hole metrics have conical singularities. By uplifting the solutions to $D=11$ supergravity using a regular Sasaki-Einstein $7$-manifold, $SE_7$, we show how the free parameters can be chosen to eliminate the conical singularities. Topologically, the $D=11$ solutions incorporate an $SE_7$ fibration over a two-dimensional weighted projective space, $mathbb{WCP}^1_{[n_-,n_+]}$, also known as a spindle, which is labelled by two integers that determine the conical singularities of the $D=4$ metrics. We also discuss the supersymmetric and extremal limit and show that the near horizon limit gives rise to a new family of regular supersymmetric $AdS_2times Y_9$ solutions of $D=11$ supergravity, which generalise a known family by the addition of a rotation parameter. We calculate the entropy of these black holes and argue that it should be possible to derive this from certain ${cal N}=2$, $d=3$ quiver gauge theories compactified on a spinning spindle with appropriate magnetic flux.
We investigate the holographic entanglement entropy in the Rindler-AdS space-time to obtain an exact solution for the corresponding minimal surface. Moreover, the holographic entanglement entropy of the charged single accelerated AdS Black holes in four dimensions is investigated. We obtain the volume of the codimension one-time slice in the bulk geometry enclosed by the minimal surface for both the RindlerAdS space-time and the charged accelerated AdS Black holes in the bulk. It is shown that the holographic entanglement entropy and the volume enclosed by the minimal hyper-surface in both the Rindler spacetime and the charged single accelerated AdS Black holes (C-metric) in the bulk decrease with increasing acceleration parameter. Behavior of the entanglement entropy, subregion size and value of the acceleration parameter are investigated. It is shown that for jAj < 0:2 a larger subregion on the boundary is equivalent to less information about the space-time.
We generalize the first law of black hole mechanics to the rotating, charged C-metric and to the Ernst metric, both of which have the charged C-metric as a special case. All of these metrics are (3+1)-dimensional, have vanishing cosmological constant, and physically describe a pair of black holes pulled apart to null infinity by some external force. Our first laws are global in the sense of applying to an entire patch of spacetime, as opposed to a neighborhood of the black hole. They are formulated with respect to boost time, whose primacy is motivated by the celestial holographic approach to scattering amplitudes.
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.
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