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Black Hole Entropy Function, Attractors and Precision Counting of Microstates
, 2007
"... In these lecture notes we describe recent progress in our understanding of attractor mechanism and entropy of extremal black holes based on the entropy function formalism. We also describe precise computation of the microscopic degeneracy of a class of quarter BPS dyons in N = 4 supersymmetric strin ..."
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Cited by 326 (28 self)
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In these lecture notes we describe recent progress in our understanding of attractor mechanism and entropy of extremal black holes based on the entropy function formalism. We also describe precise computation of the microscopic degeneracy of a class of quarter BPS dyons in N = 4 supersymmetric string theories, and compare the statistical entropy of these dyons, expanded in inverse powers of electric and magnetic charges, with a similar expansion of the corresponding black hole entropy. This comparison is extended to include the contribution to the entropy from multicentered black holes as well.
Holographic Entanglement Entropy: An Overview
, 2009
"... In this article, we review recent progresses on the holographic understandings of the entanglement entropy in the AdS/CFT correspondence. After reviewing the general idea of holographic entanglement entropy, we will explain its applications to confinement/deconfinement phase transitions, black hole ..."
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Cited by 124 (9 self)
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In this article, we review recent progresses on the holographic understandings of the entanglement entropy in the AdS/CFT correspondence. After reviewing the general idea of holographic entanglement entropy, we will explain its applications to confinement/deconfinement phase transitions, black hole entropy and covariant formulation of holography.
Nearhorizon symmetries of extremal black holes
, 2008
"... Recent work has demonstrated an attractor mechanism for extremal rotating black holes subject to the assumption of a nearhorizon SO(2, 1) symmetry. We prove the existence of this symmetry for any extremal black hole with the same number of rotational symmetries as known four and five dimensional so ..."
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Cited by 117 (10 self)
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Recent work has demonstrated an attractor mechanism for extremal rotating black holes subject to the assumption of a nearhorizon SO(2, 1) symmetry. We prove the existence of this symmetry for any extremal black hole with the same number of rotational symmetries as known four and five dimensional solutions (including black rings). The result is valid for a general twoderivative theory of gravity coupled to abelian vectors and uncharged scalars, allowing for a nontrivial scalar potential. We prove that it remains valid in the presence of higherderivative corrections. We show that SO(2, 1)symmetric nearhorizon solutions can be analytically continued to give SU(2)symmetric black hole solutions. For example, the nearhorizon limit of an extremal 5D MyersPerry black hole is related by analytic continuation to a nonextremal cohomogeneity1 MyersPerry solution.
Moduli and (un)attractor black hole thermodynamics
, 2007
"... We investigate fourdimensional spherically symmetric black hole solutions in gravity theories with massless, neutral scalars nonminimally coupled to gauge fields. In the nonextremal case, we explicitly show that, under the variation of the moduli, the scalar charges appear in the first law of bla ..."
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Cited by 59 (9 self)
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We investigate fourdimensional spherically symmetric black hole solutions in gravity theories with massless, neutral scalars nonminimally coupled to gauge fields. In the nonextremal case, we explicitly show that, under the variation of the moduli, the scalar charges appear in the first law of black hole thermodynamics. In the extremal limit, the near horizon geometry is AdS2 ×S 2 and the entropy does not depend on the values of moduli at infinity. We discuss the attractor behaviour by using Sen’s entropy function formalism as well as the effective potential approach and their relation with the results previously obtained through special geometry method. We also argue that the attractor mechanism is at the basis of the matching between the microscopic and macroscopic entropies for the extremal nonBPS KaluzaKlein black hole.
Arithmetic of Quantum Entropy Function
, 903
"... Quantum entropy function is a proposal for computing the entropy associated with the horizon of a black hole in the extremal limit, and is related via AdS/CFT correspondence to the dimension of the Hilbert space in a dual quantum mechanics. We show that in N = 4 supersymmetric string theories, quant ..."
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Cited by 36 (14 self)
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Quantum entropy function is a proposal for computing the entropy associated with the horizon of a black hole in the extremal limit, and is related via AdS/CFT correspondence to the dimension of the Hilbert space in a dual quantum mechanics. We show that in N = 4 supersymmetric string theories, quantum entropy function formalism naturally explains the origin of the subtle differences between the microscopic degeneracies of quarter BPS dyons carrying different torsion, ı.e. different arithmetical properties. These arise from additional saddle points in the path integral – whose existence depends on the arithmetical properties of the black hole charges – constructed as freely acting orbifolds of the original AdS2 × S 2 near horizon geometry. During this analysis we demonstrate that the quantum entropy function is insensitive to the details of the infrared cutoff used in the computation, and the details of the boundary terms added to the action. We also discuss the role of the asymptotic symmetries of AdS2 in carrying out the path integral in the definition of quantum entropy function. Finally we show that even though quantum entropy function is expected to compute the absolute degeneracy in a given charge and angular momentum sector, it can also be used to compute
Quantum Entropy Function from AdS(2)/CFT(1) Correspondence
, 2008
"... We review and extend recent attempts to find a precise relation between extremal black hole entropy and degeneracy of microstates using AdS2/CFT1 correspondence. Our analysis leads to a specific relation between degeneracy of black hole microstates and an appropriately defined partition function of ..."
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Cited by 34 (9 self)
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We review and extend recent attempts to find a precise relation between extremal black hole entropy and degeneracy of microstates using AdS2/CFT1 correspondence. Our analysis leads to a specific relation between degeneracy of black hole microstates and an appropriately defined partition function of string theory on the near horizon geometry, – named the quantum entropy function. In the classical limit this reduces to the usual relation between statistical
Precision entropy of spinning black holes
 JHEP 0709, 003 (2007) [arXiv:0705.1847 [hepth
"... We construct spinning black hole solutions in five dimensions that take into account the mixed gaugegravitational ChernSimons term and its supersymmetric completion. The resulting entropy formula is discussed from several points of view. We include a TaubNUT base space in order to test recent con ..."
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Cited by 22 (3 self)
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We construct spinning black hole solutions in five dimensions that take into account the mixed gaugegravitational ChernSimons term and its supersymmetric completion. The resulting entropy formula is discussed from several points of view. We include a TaubNUT base space in order to test recent conjectures relating 5D black holes to 4D black holes and the topological string. Our explicit results show that certain charge shifts have to be taken into account for these relations to hold. We also compute corrections to the entropy of black rings in terms of near horizon data.