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58
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.
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.
Stationary black holes and attractor mechanism, Nucl. Phys. B794
, 2008
"... We investigate the symmetries of the near horizon geometry of extremal stationary black hole in four dimensional Einstein gravity coupled to abelian gauge fields and neutral scalars. Careful consideration of the equations of motion and the boundary conditions at the horizon imply that the near horiz ..."
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Cited by 38 (2 self)
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We investigate the symmetries of the near horizon geometry of extremal stationary black hole in four dimensional Einstein gravity coupled to abelian gauge fields and neutral scalars. Careful consideration of the equations of motion and the boundary conditions at the horizon imply that the near horizon geometry has SO(2, 1) × U(1) isometry. This compliments the rotating attractors proposal of hepth/0606244 which had assumed the presence of this isometry. The extremal solutions are classified into two families differentiated by the presence or absence of an ergoregion. We also comment on the attractor mechanism of both branches.
Nonsupersymmetric Black Holes and Topological Strings
, 2007
"... We study nonsupersymmetric, extremal 4 dimensional black holes which arise upon compactification of type II superstrings on CalabiYau threefolds. We propose a generalization of the OSV conjecture for higher derivative corrections to the nonsupersymmetric black hole entropy, in terms of the one pa ..."
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Cited by 18 (1 self)
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We study nonsupersymmetric, extremal 4 dimensional black holes which arise upon compactification of type II superstrings on CalabiYau threefolds. We propose a generalization of the OSV conjecture for higher derivative corrections to the nonsupersymmetric black hole entropy, in terms of the one parameter refinement of topological string introduced by Nekrasov. We also study the attractor mechanism for nonsupersymmetric black holes and show how the inverse problem of fixing charges in terms of the attractor value of CY moduli can be explicitly solved.
Nonsupersymmetric Attractors in BornInfeld Black Holes with A Cosmological Constant
, 2007
"... We investigate the attractor mechanism for spherically symmetric extremal black holes in EinsteinBornInfelddilaton theory of gravity in fourdimensions, in the presence of a cosmological constant. We look for solutions analytic near the horizon by using perturbation method. It is shown that the v ..."
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Cited by 18 (0 self)
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We investigate the attractor mechanism for spherically symmetric extremal black holes in EinsteinBornInfelddilaton theory of gravity in fourdimensions, in the presence of a cosmological constant. We look for solutions analytic near the horizon by using perturbation method. It is shown that the values of the scalar fields at the horizon are only dependent on the charges carried by the black hole and are irrelevant in the asymptotic values. This analysis supports the validity of nonsupersymmetric attractors in the presence of higher derivative interactions in the gauge fields part and in nonasymptotically flat spacetime.
On R 2 corrections for 5D black holes
 JHEP 0708
, 2007
"... We study higher order corrections to extremal black holes/black string in five dimensions. These higher order corrections are due to supersymmetric completion of R 2 term in five dimensions. By making use of the results we extend the notion of very special geometry when higher derivative terms are a ..."
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Cited by 15 (0 self)
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We study higher order corrections to extremal black holes/black string in five dimensions. These higher order corrections are due to supersymmetric completion of R 2 term in five dimensions. By making use of the results we extend the notion of very special geometry when higher derivative terms are also taken into account. This can be used to make a connection between total bundle space of near horizon wrapped M2’s and wrapped M5’s in the presence of higher order corrections. We also show how the corrected geometry removes the singularity of a small black hole. 1
The Attractor mechanism in GaussBonnet gravity
"... We study extremal black hole solutions of D = 5 GaussBonnet gravity coupled to a system of gauge and scalar fields. As in Einstein gravity, we find that the values of the scalar fields on the horizon must extremize a certain effective potential that depends on the black hole charges. If the matrix ..."
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Cited by 13 (0 self)
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We study extremal black hole solutions of D = 5 GaussBonnet gravity coupled to a system of gauge and scalar fields. As in Einstein gravity, we find that the values of the scalar fields on the horizon must extremize a certain effective potential that depends on the black hole charges. If the matrix of second derivatives of the effective potential at this extremum has positive eigenvalues, we give evidence, based on a near horizon perturbative expansion, that the attractor mechanism continues to hold in this general class of theories. We numerically construct solutions to a particular simple single scalar field model that display the attractor mechanism over a wide range of asymptotic values for the scalar field. We also numerically construct nonextremal solutions and show that the attractor mechanism fails to hold away from extremality.