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65
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.
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.
Holography of Charged Dilaton Black Holes
 Black Branes,” JHEP
, 2010
"... Abstract: We study charged dilaton black branes in AdS4. Our system involves a dilaton φ coupled to a Maxwell field Fµν with dilatondependent gauge coupling, 1 g2 = f 2(φ). First, we find the solutions for extremal and near extremal branes through a combination of analytical and numerical technique ..."
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Cited by 22 (4 self)
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Abstract: We study charged dilaton black branes in AdS4. Our system involves a dilaton φ coupled to a Maxwell field Fµν with dilatondependent gauge coupling, 1 g2 = f 2(φ). First, we find the solutions for extremal and near extremal branes through a combination of analytical and numerical techniques. The near horizon geometries in the simplest cases, where f(φ) = eαφ, are Lifshitzlike, with a dynamical exponent z determined by α. The black hole thermodynamics varies in an interesting way with α, but in all cases the entropy is vanishing and the specific heat is positive for the near extremal solutions. We then compute conductivity in these backgrounds. We find that somewhat surprisingly, the AC conductivity vanishes like ω2 at T = 0 independent of α. We also explore the charged black brane physics of several other classes of gaugecoupling functions f(φ). In addition to possible applications in AdS/CMT, the extremal black branes are of interest from the point of view of the attractor mechanism. The near horizon geometries for these branes are universal, independent of the asymptotic values of the moduli, and describe generic classes of endpoints for attractor flows which are different from AdS2 ×R2. ar X iv
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
Instantons, black holes and harmonic functions,” arXiv:0906.3451 [hepth
"... Abstract: We find a class of fivedimensional EinsteinMaxwell type Lagrangians which contains the bosonic Lagrangians of vector multiplets as a subclass, and preserves some features of supersymmetry, namely the existence of multicentered black hole solutions and of attractor equations. Solutions c ..."
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Cited by 12 (3 self)
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Abstract: We find a class of fivedimensional EinsteinMaxwell type Lagrangians which contains the bosonic Lagrangians of vector multiplets as a subclass, and preserves some features of supersymmetry, namely the existence of multicentered black hole solutions and of attractor equations. Solutions can be expressed in terms of harmonic functions through a set of algebraic equations. The geometry underlying these Lagrangians is characterised by the existence of a Hesse potential and generalizes the very special real geometry of vector multiplets. Our construction proceeds by first obtaining instanton solutions for a class of fourdimensional Euclidean sigma models, which includes those occuring for fourdimensional Euclidean N = 2 vector multiplets as a subclass. For solutions taking values in a completely isotropic submanifold of the target space, we show that the solution can be expressed in terms of harmonic functions if an integrability condition is met. This condition can either be solved by imposing that the solution depends on a single coordinate, or by imposing that the target space is a paraKähler manifold which can be obtained from a real Hessian manifold by a generalized rmap. In the latter case one obtains multicentered solutions.
Entropy Function for NonExtremal Black Holes in String Theory
, 2007
"... We generalize the entropy function formalism to fivedimensional and fourdimensional nonextremal black holes in string theory. In the near horizon limit, these black holes have BTZ metric as part of the spacetime geometry. It is shown that the entropy function formalism also works very well for t ..."
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Cited by 12 (1 self)
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We generalize the entropy function formalism to fivedimensional and fourdimensional nonextremal black holes in string theory. In the near horizon limit, these black holes have BTZ metric as part of the spacetime geometry. It is shown that the entropy function formalism also works very well for these nonextremal black holes and it can reproduce the BekensteinHawking entropy of these black holes in