Black hole entropy function, attractors and precision counting of microstates
2007/08/31 by Ashoke Sen · 481 citations
Mathematics · Physics and Astronomy · #Attractor #Binary entropy function #Black Holes and Theoretical Physics #Black hole thermodynamics #Cosmology and Gravitation Theories #Entropy (arrow of time) #Extremal black hole #Galaxies: Formation, Evolution, Phenomena #Mathematical analysis #Mathematical physics #Mathematics #Physics #Principle of maximum entropy #Quantum mechanics #Statistical physics #String theory #Theoretical physics #hep-th
paper · pdf · doi:10.1007/s10714-008-0626-4
published in General Relativity and Gravitation 40(11), 2249-2431 (Springer Science+Business Media) · LaTeX file, 196 pages, based on lectures given at various schools; v2: added appendix E containing analysis of the multiple D5-brane system, expanded discussion on duality orbits, other minor changes, references added; v3: equations (5.6.20) and (5.6.21) corrected; v4: minor corrections to equations (C.19), (C.20)
openalex publication_date 2008/04/11 · arxiv created 2009/11/05 · arxiv updated 2010/04/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Abstract
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 multi-centered black holes as well.
Citations
- Non-Supersymmetric Unattractors in Born-Infeld Black Holes
- Heterotic Coset Models of Microscopic Strings and Black Holes
- Crossing the Wall: Branes vs. Bundles
- Nearing the Horizon of a Heterotic String
- Les Houches Lectures on Strings and Arithmetic
- Re-Recounting Dyons in N=4 String Theory
- From BPS to Non-BPS Black Holes Canonically
- Black hole in three-dimensional spacetime
- On the correspondence between D-branes and stationary supergravity solutions of type II Calabi-Yau compactifications
- Three-Dimensional Gravity Revisited
- BLACK HOLE ENTROPY IN HIGHER CURVATURE GRAVITY
- String theory and noncommutative geometry
- Dyon spectrum in CHL models
- On entropy function for supersymmetric black rings
- Flow equations for non-BPS extremal black holes
- R4corrections toD1D5pblack hole entropy from entropy function formalism
- String theory dynamics in various dimensions
- Precision Microstate Counting of Small Black Rings
- Lectures on black holes, topological strings and quantum attractors
- Magnetic monopoles in Kaluza-Klein theories
- Fundamental superstrings as holograms
- D--branes and Spinning Black Holes
- The elliptic genus of Calabi-Yau 3- and 4-folds, product formulae and generalized Kac-Moody algebras
- Instantons on Noncommutative ℝ 4 , and (2,0) Superconformal Six Dimensional Theory
- Magnetic monopoles in string theory
- 2 + 1 dimensional gravity as an exactly soluble system
- Stationary black holes and attractor mechanism
- Black Hole Entropy, Special Geometry and Strings
- Black hole microstates and attractor without supersymmetry
- Algebras, BPS states, and strings
- Order α′ (two-loop) equivalence of the string equations of motion and the σ-model Weyl invariance conditions
- One entropy function to rule them all…
- Entropy function for non-extremal black holes in string theory
- A note on D1-D5-J system and 5D small black ring
- Non-supersymmetric attractors in string theory
- Gravitation, gauge theories and differential geometry
- Spectrum of dyons and black holes in CHL orbifolds using Borcherds lift
- 5D attractors with higher derivatives
- Black hole entropy function and the attractor mechanism in higher derivative gravity
- Nonsupersymmetric attractors
- Split attractor flows and the spectrum of BPS D-branes on the quintic
- Exploring the relation between 4D and 5D BPS solutions
- Comments on the spectrum of CHL dyons
- Moduli dependence of string loop corrections to gauge coupling constants
- Walls of marginal stability and dyon spectrum in Script N = 4 supersymmetric string theories
- Central charges in the canonical realization of asymptotic symmetries: An example from three dimensional gravity
- Extremal non-BPS black holes and entropy extremization
- Rotating Kaluza-Klein Black Holes
- Automorphic forms onO s +2,2(R) and infinite products
- Three-Dimensional Massive Gauge Theories
- Some properties of the Noether charge and a proposal for dynamical black hole entropy
- STRONG–WEAK COUPLING DUALITY IN FOUR-DIMENSIONAL STRING THEORY
- Black hole entropy in the presence of Chern–Simons terms
- Lovelock type gravity and small black holes in heterotic string theory
- α′-Corrections to extremal dyonic black holes in heterotic string theory
- Microscopic Origin of the Bekenstein-Hawking Entropy
- Elliptic Genera of Symmetric Products and Second Quantized Strings
- Noncompact symmetries in string theory
- Unity of superstring dualities
- Critical points of the Black-Hole potential for homogeneous special geometries
- Counting dyons in N = 4 string theory
- Entropy function and attractors for AdS black holes
- Dyon spectrum in Script N = 4 supersymmetric type II string theories
- Strings, higher curvature corrections, and black holes
- Counting dyons in Script N = 8 string theory
- The large N limit of superconformal field theories and supergravity
- Topologically massive gauge theories
Cited by