On Wald entropy of black holes: logarithmic corrections and trace anomaly

Abstract

Quantum effects due to conformal matter in a black hole background result in universal logarithmic corrections to black-hole entropy. The universality resides in the connection of the log term coefficient with those of type-A and type-B Weyl anomalies, regularization-scheme independent quantities. We presently study the case of extremal black holes within Wald's Noether charge formalism. In the conformal class of flat metrics, we are again able to unveil the log term in the entropy from the horizon value of the solution to the Q-curvature uniformization problem. Beyond conformally flat backgrounds, type-B Weyl anomaly becomes an obstruction to considering flat space as the fiducial metric and the search for a metric of constant Q-curvature remains open. Notwithstanding, by a uniform scaling argument we show that the results based on heat kernel and euclidean computations (namely entropy function and conical defect) can also be derived as Wald entropy, that is, as Noether charge of the integrated anomaly or conformal index. We finally comment on the relation with entanglement entropy.

10 pages, minor changes

References in corpus (37)

• Black Hole Entropy is Noether Charge
• Aspects of Holographic Entanglement Entropy
• On Renormalization Group Flows in Four Dimensions
• On Black Hole Entropy
• Black Hole Entropy in M-Theory
• Holographic c-theorems in arbitrary dimensions
• Black Hole Entropy Function and the Attractor Mechanism in Higher Derivative Gravity
• Geometric Classification of Conformal Anomalies in Arbitrary Dimensions
• Hawking Radiation and Black Hole Thermodynamics
• A Quartic Conformally Covariant Differential Operator for Arbitrary Pseudo-Riemannian Manifolds (Summary)
• Entanglement entropy, conformal invariance and extrinsic geometry
• Corrections to macroscopic supersymmetric black-hole entropy
• Quantum Entropy Function from AdS(2)/CFT(1) Correspondence
• On Holographic Entanglement Entropy and Higher Curvature Gravity
• Universality of Quantum Entropy for Extreme Black Holes
• Logarithmic Corrections to N=2 Black Hole Entropy: An Infrared Window into the Microstates
• Black Holes in Gravity with Conformal Anomaly and Logarithmic Term in Black Hole Entropy
• Entropy Function for Heterotic Black Holes
• Black holes with topologically nontrivial AdS asymptotics
• Logarithmic Corrections to N=4 and N=8 Black Hole Entropy: A One Loop Test of Quantum Gravity
• On one-loop renormalization of black-hole entropy
• Quantum Tunneling and Trace Anomaly
• Logarithmic Corrections to Extremal Black Hole Entropy from Quantum Entropy Function
• Distributional Geometry of Squashed Cones
• On "Non-Geometric" Contribution To The Entropy Of Black Hole Due To Quantum Corrections
• Logarithmic Corrections to Rotating Extremal Black Hole Entropy in Four and Five Dimensions
• Spontaneous Breaking of Conformal Invariance and Trace Anomaly Matching
• Macroscopic Effects of the Quantum Trace Anomaly
• One-loop Renormalization of Black Hole Entropy Due to Non-minimally Coupled Matter
• Exact Differential and Corrected Area Law for Stationary Black Holes in Tunneling Method
• A comment on black hole entropy or does Nature abhor a logarithm?
• Vacuum polarization in Schwarzschild space-time by anomaly induced effective actions
• Geometry of nonextreme black holes near the extreme state
• Black Hole Microstate Counting and its Macroscopic Counterpart
• Heat Kernel Expansion and Extremal Kerr-Newmann Black Hole Entropy in Einstein-Maxwell Theory
• Logarithmic correction to BH entropy as Noether charge
• Analysing Charges in even dimensions

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• Quantum corrections to a finite temperature BIon
• Quantum Thermodynamics of an M2-M5 Brane System
• Simple regular black hole with logarithmic entropy correction
• Logarithmic correction to the entropy of a Kerr-Newman family of black holes in $U(1{)}^2$-charged STU supergravity models
• The boundary effect of anomaly-induced action
• QED trace anomaly, non-local Lagrangians and quantum Equivalence Principle violations