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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 324 (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.
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 114 (8 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.
Holographic gravitational anomalies
 JHEP
, 2006
"... In the AdS/CFT correspondence one encounters theories that are not invariant under diffeomorphisms. In the boundary theory this is a gravitational anomaly, and can arise in 4k + 2 dimensions. In the bulk, there can be gravitational ChernSimons terms which vary by a total derivative. We work out the ..."
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Cited by 102 (7 self)
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In the AdS/CFT correspondence one encounters theories that are not invariant under diffeomorphisms. In the boundary theory this is a gravitational anomaly, and can arise in 4k + 2 dimensions. In the bulk, there can be gravitational ChernSimons terms which vary by a total derivative. We work out the holographic stress tensor for such theories, and demonstrate agreement between the bulk and boundary. Anomalies lead to novel effects, such as a nonzero angular momentum for global AdS3. In string theory such ChernSimons terms are known with exact coefficients. The resulting anomalies, combined with symmetries, imply corrections to the BekensteinHawking entropy of black holes that agree exactly with the microscopic counting.
The NonBPS Black Hole Attractor Equation
, 2008
"... We study the attractor mechanism for extremal nonBPS black holes with an infinite throat near horizon geometry, developing, as we do so, a physical argument as to why such a mechanism does not exist in nonextremal cases. We present a detailed derivation of the nonsupersymmetric attractor equati ..."
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Cited by 65 (3 self)
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We study the attractor mechanism for extremal nonBPS black holes with an infinite throat near horizon geometry, developing, as we do so, a physical argument as to why such a mechanism does not exist in nonextremal cases. We present a detailed derivation of the nonsupersymmetric attractor equation. This equation defines the stabilization of moduli near the black hole horizon: the fixed moduli take values specified by electric and magnetic charges corresponding to the fluxes in a Calabi Yau compactification of string theory. They also define the socalled doubleextremal solutions. In some examples, studied previously by Tripathy and Trivedi, we solve the equation and show that the moduli are fixed at values which may also be derived from the critical points of the black hole
Rotating Attractors
, 2006
"... We prove that, in a general higher derivative theory of gravity coupled to abelian gauge fields and neutral scalar fields, the entropy and the near horizon background of a rotating extremal black hole is obtained by extremizing an entropy function which depends only on the parameters labeling the ne ..."
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Cited by 63 (19 self)
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We prove that, in a general higher derivative theory of gravity coupled to abelian gauge fields and neutral scalar fields, the entropy and the near horizon background of a rotating extremal black hole is obtained by extremizing an entropy function which depends only on the parameters labeling the near horizon background and the electric and magnetic charges and angular momentum carried by the black hole. If the entropy function has a unique extremum then this extremum must be independent of the asymptotic values of the moduli scalar fields and the solution exhibits attractor behaviour. If the entropy function has flat directions then the near horizon background is not uniquely determined by the extremization equations and could depend on the asymptotic data on the moduli fields, but the value of the entropy is still independent of this asymptotic data. We illustrate these results in the context of two derivative theories of gravity in several examples. These include Kerr black hole, KerrNewman black hole, black holes in KaluzaKlein theory, and
Lectures on on black holes, topological strings and quantum attractors
, 2006
"... Preprint typeset in JHEP style PAPER VERSION hepth/0607227 ..."
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Cited by 62 (10 self)
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Preprint typeset in JHEP style PAPER VERSION hepth/0607227
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.
Nonsupersymmetric attractors and entropy function,” JHEP 0603, 003 (2006
 in N = 2 supergravity,” arXiv:hepth/0603149. G. Exirifard, “The
"... We study the entropy of nonsupersymmetric extremal black holes which exhibit attractor mechanism by making use of the entropy function. This method, being simple, can be used to calculate corrections to the entropy due to higher order corrections to the action. In particular we apply this method fo ..."
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Cited by 53 (2 self)
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We study the entropy of nonsupersymmetric extremal black holes which exhibit attractor mechanism by making use of the entropy function. This method, being simple, can be used to calculate corrections to the entropy due to higher order corrections to the action. In particular we apply this method for five dimensional nonsupersymmetric extremal black hole which carries two magnetic charges and find the R 2 corrections to the entropy. Using the behavior of the action evaluated for the extremal black hole near the horizon, we also present a simple expression for Cfunction corrected by higher order corrections.
Domain walls and superpotentials from M theory on Calabi
 Yau threefolds,” Nucl. Phys. B580 (2000) 225–242, http://arXiv.org/abs/hepth/0001082
"... Compactification of M theory in the presence of Gfluxes yields N = 2 fivedimensional gauged supergravity with a potential that lifts all supersymmetric vacua. We derive the effective superpotential directly from the KaluzaKlein reduction of the elevendimensional action on a CalabiYau threefold ..."
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Cited by 48 (5 self)
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Compactification of M theory in the presence of Gfluxes yields N = 2 fivedimensional gauged supergravity with a potential that lifts all supersymmetric vacua. We derive the effective superpotential directly from the KaluzaKlein reduction of the elevendimensional action on a CalabiYau threefold and compare it with the superpotential obtained by means of calibrations. We discuss an explicit domain wall solution, which represents fivebranes wrapped over holomorphic cycles. This solution has a “running volume ” and we comment on the possibility that quantum corrections provide a lower bound allowing for an AdS5 vacuum of the 5dimensional supergravity