Stretching the Horizon of a Higher Dimensional Small Black Hole

Abstract

There is a general scaling argument that shows that the entropy of a small black hole, representing a half-BPS excitation of an elementary heterotic string in any dimension, agrees with the statistical entropy up to an overall numerical factor. We propose that for suitable choice of field variables the near horizon geometry of the black hole in D space-time dimensions takes the form of AdS_2\times S^{D-2} and demonstrate how this ansatz can be used to calculate the numerical factor in the expression for the black hole entropy if we know the higher derivative corrections to the action. We illustrate this by computing the entropy of these black holes in a theory where we modify the supergravity action by adding the Gauss-Bonnet term. The black hole entropy computed this way is finite and has the right dependence on the charges in accordance with the general scaling argument, but the overall numerical factor does not agree with that computed from the statistical entropy except for D=4 and D=5. This is not surprising in view of the fact that we do not use a fully supersymmetric action in our analysis; however this analysis demonstrates that higher derivative corrections are capable of stretching the horizon of a small black hole in arbitrary dimensions.

arXiv commentLaTeX file, 26 pages; v2: a simple expression for entropy is given and references added

References in corpus (30)

• Black Hole Entropy is Noether Charge
• Some Properties of Noether Charge and a Proposal for Dynamical Black Hole Entropy
• N=2 Extremal Black Holes
• Black Hole Entropy in Canonical Quantum Gravity and Superstring Theory
• Supersymmetry and Attractors
• On Black Hole Entropy
• Black Hole Entropy in M-Theory
• Macroscopic Entropy of $N=2$ Extremal Black Holes
• Black Hole Thermodynamics and Negative Entropy in deSitter and Anti-deSitter Einstein-Gauss-Bonnet gravity
• EXTREMAL BLACK HOLES AND ELEMENTARY STRING STATES
• Corrections to macroscopic supersymmetric black-hole entropy
• Black Hole Solutions in Heterotic String Theory on a Torus
• Twisting Classical Solutions in Heterotic String Theory
• Macroscopic entropy formulae and non-holomorphic corrections for supersymmetric black holes
• On singularities of spherically symmetric backgrounds in string theory
• A Stringy Cloak for a Classical Singularity
• How Does a Fundamental String Stretch its Horizon?
• Asymptotic level density in heterotic string theory and rotating black holes
• Fivebrane Instantons and $R^2$ couplings in $N=4$ String Theory
• Higher-Order Black-Hole Solutions in N=2 Supergravity and Calabi-Yau String Backgrounds
• String-Corrected Black Holes
• Entropy and supersymmetry of $D$ dimensional extremal electric black holes versus string states
• Area law corrections from state counting and supergravity
• N=2 Electric-magnetic duality in a chiral background
• N=2 symplectic reparametrizations in a chiral background
• Extremal black holes as exact string solutions
• Examples of stationary BPS solutions in N=2 supergravity theories with R^2-interactions
• On alpha'-corrections to D-brane solutions
• Black holes and Elementary String States in N=2 Supersymmetric String Theories
• Two and three loop alpha' corrections to T-duality: Kasner and Schwarzschild

Cited by in corpus (59)

• Black Hole Entropy Function and the Attractor Mechanism in Higher Derivative Gravity
• Black Hole Entropy Function, Attractors and Precision Counting of Microstates
• Near-horizon symmetries of extremal black holes
• Non-Supersymmetric Attractors
• Microscopic Black Hole Entropy in Theories with Higher Derivatives
• Holographic Gravitational Anomalies
• Non-Supersymmetric Attractors in String Theory
• Entropy Function for Heterotic Black Holes
• The Library of Babel: On the origin of gravitational thermodynamics
• Black Hole Microstates and Attractor Without Supersymmetry
• Strings, Black Holes, and Quantum Information
• Exact Black Hole Degeneracies and the Topological String
• BPS Black Hole Degeneracies and Minimal Automorphic Representations
• General 2 charge geometries
• New Attractors, Entropy Function and Black Hole Partition Function
• Non-Supersymmetric Attractors in $R^2$ Gravities
• Topological strings and large N phase transitions II: Chiral expansion of q-deformed Yang-Mills theory
• Two Charge System Revisited: Small Black Holes or Horizonless Solutions?
• Fundamental Strings, Holography, and Nonlinear Superconformal Algebras
• EVH Black Holes, AdS3 Throats and EVH/CFT Proposal
• R^4 Corrections to D1D5p Black Hole Entropy from Entropy Function Formalism
• Spinning Strings as Small Black Rings
• Lovelock type gravity and small black holes in heterotic string theory
• New attractor mechanism for spherically symmetric extremal black holes
• Extremal single-charge small black holes: Entropy function analysis
• Fundamental Superstrings as Holograms
• alpha'-exact entropies for BPS and non-BPS extremal dyonic black holes in heterotic string theory from ten-dimensional supersymmetry
• Topological strings and large N phase transitions I: Nonchiral expansion of q-deformed Yang-Mills theory
• Entropy of an extremal regular black hole
• Entropy Function for 4-Charge Extremal Black Holes in Type IIA Superstring Theory
• On Entropy Function for Supersymmetric Black Rings
• Weak Gravity Conjecture, Black Hole Entropy, and Modular Invariance
• A Note on D1-D5-J System and 5D Small Black Ring
• Entropy Function for Non-Extremal Black Holes in String Theory
• The alpha-prime stretched horizon in the Heterotic string
• Extremal black holes in D=5: SUSY vs. Gauss-Bonnet corrections
• Non-supersymmetric Attractors in Born-Infeld Black Holes with a Cosmological Constant
• On the Entropy Function and the Attractor Mechanism for Spherically Symmetric Extremal Black Holes
• Entropy Function and Universality of Entropy-Area Relation for Small Black Holes
• Flow of Geometries and Instantons on the Null Orbifold
• Black-holes, topological strings and large N phase transitions
• Two-charge small black hole entropy: String-loops and multi-strings
• State-space Correlations and Stabilities
• From Fundamental Strings to Small Black Holes
• Features of warped geometry in presence of Gauss-Bonnet coupling
• Fundamental Plasmid Strings and Black Rings
• Superconformal Quantum Mechanics of Small Black Holes
• Equivalence of JT Gravity and Near-extremal Black Hole Dynamics in Higher Derivative Theory
• Quantum M-wave and Black 0-brane
• Near-horizon brane-scan revived
• Thermodynamic Geometry and Hawking Radiation
• Special Geometry, Hessian Structures and Applications
• Black hole entropy, flat directions and higher derivatives
• A Toy Model for Topology Change Transitions: Role of Curvature Corrections
• Coarse-Graining the Lin-Maldacena Geometries
• On small black holes, KK monopoles and solitonic 5-branes
• Are There Four-Dimensional Small Black Rings?
• Type II Small Stringy Black Holes, Probe Branes and Higher Derivative Interactions
• On 5D Small Black Holes