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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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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.
Geometric Perspective of Entropy Function
 Embeddings, Spectrum and Convexity; LAP Academic Publication
, 2011
"... ar ..."
DoubleHorizon Limit, AdS Geometry and Entropy Function
, 2007
"... We start from a generic metric which describes four dimensional stationary black holes in an arbitrary theory of gravity and show that the AdS2 part of the near horizon geometry is a consequence of the doublehorizon limit and finiteness. We also show that the field configurations of the near horizo ..."
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We start from a generic metric which describes four dimensional stationary black holes in an arbitrary theory of gravity and show that the AdS2 part of the near horizon geometry is a consequence of the doublehorizon limit and finiteness. We also show that the field configurations of the near horizon are determined if the same conditions are applied to the equations of motion. This is done by showing that in the doublehorizon limit field equations at the horizon decouple from the bulk of the space. Solving these equations gives the near horizon field configurations. It is shown that these decoupled equations can be obtained from an action derived from the original action by applying the doublehorizon
StateSpace Geometry, Statistical Fluctuations, and Black Holes in String Theory
"... We study the statespace geometry of various extremal and nonextremal black holes in string theory. From the notion of the intrinsic geometry, we offer a statespace perspective to the black hole vacuum fluctuations. For a given black hole entropy, we explicate the intrinsic geometric meaning of th ..."
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We study the statespace geometry of various extremal and nonextremal black holes in string theory. From the notion of the intrinsic geometry, we offer a statespace perspective to the black hole vacuum fluctuations. For a given black hole entropy, we explicate the intrinsic geometric meaning of the statistical fluctuations, local and global stability conditions, and long range statistical correlations. We provide a set of physical motivations pertaining to the extremal and nonextremal black holes, namely, the meaning of the chemical geometry and physics of correlation. We illustrate the statespace configurations for general charge extremal black holes. In sequel, we extend our analysis for various possible charge and anticharge nonextremal black holes. From the perspective of statistical fluctuation theory, we offer general remarks, future directions, and open issues towards the intrinsic geometric understanding of the vacuum fluctuations and black holes in string theory.