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 (11)

• Holographic c-theorems in arbitrary dimensions
• A Quartic Conformally Covariant Differential Operator for Arbitrary Pseudo-Riemannian Manifolds (Summary)
• Entanglement entropy, conformal invariance and extrinsic geometry
• Quantum Entropy Function from AdS(2)/CFT(1) Correspondence
• On Holographic Entanglement Entropy and Higher Curvature Gravity
• Quantum Tunneling and Trace Anomaly
• Logarithmic Corrections to Extremal Black Hole Entropy from Quantum Entropy Function
• Distributional Geometry of Squashed Cones
• Spontaneous Breaking of Conformal Invariance and Trace Anomaly Matching
• Macroscopic Effects of the Quantum Trace Anomaly
• Exact Differential and Corrected Area Law for Stationary Black Holes in Tunneling Method

Cited by in corpus (10)

• Thermodynamics of Conformal Anomaly Corrected Black Holes in AdS Space
• Black hole thermodynamics: No inconsistency via the inclusion of the missing P-V terms
• Logarithmic Corrections to $N\ge 2$ Black Hole Entropy
• Semi-classical thermodynamics of quantum extremal surfaces in Jackiw-Teitelboim gravity
• 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