Entropy of Quantum Black Holes

Abstract

In the Loop Quantum Gravity, black holes (or even more general Isolated Horizons) are described by a SU(2) Chern-Simons theory. There is an equivalent formulation of the horizon degrees of freedom in terms of a U(1) gauge theory which is just a gauged fixed version of the SU(2) theory. These developments will be surveyed here. Quantum theory based on either formulation can be used to count the horizon micro-states associated with quantum geometry fluctuations and from this the micro-canonical entropy can be obtained. We shall review the computation in SU(2) formulation. Leading term in the entropy is proportional to horizon area with a coefficient depending on the Barbero-Immirzi parameter which is fixed by matching this result with the Bekenstein-Hawking formula. Remarkably there are corrections beyond the area term, the leading one is logarithm of the horizon area with a definite coefficient -3/2, a result which is more than a decade old now. How the same results are obtained in the equivalent U(1) framework will also be indicated. Over years, this entropy formula has also been arrived at from a variety of other perspectives. In particular, entropy of BTZ black holes in three dimensional gravity exhibits the same logarithmic correction. Even in the String Theory, many black hole models are known to possess such properties. This suggests a possible universal nature of this logarithmic correction.

References in corpus (67)

• Microscopic Origin of the Bekenstein-Hawking Entropy
• Background Independent Quantum Gravity: A Status Report
• Quantum Geometry and Black Hole Entropy
• Black hole entropy in Loop Quantum Gravity
• Black Hole Entropy from Loop Quantum Gravity
• Logarithmic correction to the Bekenstein-Hawking entropy
• A Correspondence Principle for Black Holes and Strings
• Logarithmic Corrections to Black Hole Entropy from the Cardy Formula
• General Logarithmic Corrections to Black Hole Entropy
• Black hole entropy from Quantum Geometry
• Isolated Horizons: Hamiltonian Evolution and the First Law
• Entropy from Conformal Field Theory at Killing Horizons
• Generic Isolated Horizons and their Applications
• Linking Topological Quantum Field Theory and Nonperturbative Quantum Gravity
• Universal Low-Energy Dynamics for Rotating Black Holes
• Aspects of Black Hole Quantum Mechanics and Thermodynamics in 2+1 Dimensions
• Universality of Quantum Entropy for Extreme Black Holes
• Mechanics of Isolated Horizons
• Self-gravitating fundamental strings and black-holes
• Black hole entropy and SU(2) Chern-Simons theory
• Statistical Entropy of Nonextremal Four-Dimensional Black Holes and U-Duality
• Derivation of the Verlinde Formula from Chern-Simons Theory and the G/G model
• Black hole entropy from an SU(2)-invariant formulation of Type I isolated horizons
• A String Model of Black Hole Microstates
• Quantum Black Hole Entropy
• Universal canonical black hole entropy
• An improved estimate of black hole entropy in the quantum geometry approach
• Black hole state counting in Loop Quantum Gravity: A number theoretical approach
• The Statistical Mechanics of the Three-Dimensional Euclidean Black Hole
• On Quantum Statistical Mechanics of a Schwarzschild Black Hole
• An Exact Black Hole Entropy Bound
• Detailed black hole state counting in loop quantum gravity
• Further Evidence for the Conformal Structure of a Schwarzschild Black Hole in an Algebraic Approach
• Quantum Black Holes: Entropy and Entanglement on the Horizon
• The Fine Structure of SU(2) Intertwiners from U(N) Representations
• Counting Schwarzschild and Charged Black Holes
• The SU(2) Black Hole entropy revisited
• Braneless Black Holes
• Exact Results for the BTZ Black Hole
• Entropic Inflation
• A new holographic entropy bound from quantum geometry
• Holographic actions from black hole entropy
• Algebraic approach to quantum black holes: logarithmic corrections to black hole entropy
• Chern-Simons Theory, Colored-Oriented Braids and Link invariants
• The combinatorics of the SU(2) black hole entropy in loop quantum gravity
• On the computation of black hole entropy in loop quantum gravity
• Black Hole Entropy, Loop Gravity, and Polymer Physics
• Generating functions for black hole entropy in Loop Quantum Gravity
• Polynomials for Torus Links from Chern-Simons Gauge Theories
• Schwarzschild horizon dynamics and SU(2) Chern-Simons theory
• Black hole horizons from within loop quantum gravity
• Black Hole Entropy from Spin One Punctures
• Quantum Gravity on $d{S}_3$
• Entropy of Isolated Horizons revisited
• Chern-Simons expectation values and quantum horizons from LQG and the Duflo map
• Black holes in full quantum gravity
• Universal Counting of Black Hole Entropy by Strings on the Stretched Horizon
• Universal criterion for black hole stability
• Chern-Simons theory, Stokes' Theorem, and the Duflo map
• Generalized Hawking-Page Phase Transition
• Chern-Simons Theory, Knot Invariants, Vertex Models and Three-manifold Invariants
• Three-Manifold Invariants from Chern-Simons Field Theory with Arbitrary Semi-Simple Gauge Groups
• BTZ Black Hole Entropy from Ponzano-Regge Gravity
• Black Hole Entropy from a Highly Excited Elementary String
• Asymptotic Density of Open p-brane States with Zero-modes included
• Quantized black holes, correspondence principle, and holographic bound
• Schwarz Type Topological Quantum Field Theories

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