One-loop Quantum Corrections to the Entropy for an Extremal Reissner-Nordström Black Hole

Abstract

The first quantum corrections to the entropy for an eternal 4-dimensional extremal Reissner-Nordström black hole is investigated at one-loop level, in the large mass limit of the black hole, making use of the conformal techniques related to the optical metric. A leading cubic horizon divergence is found and other divergences appear due to the singular nature of the optical manifold. The area law is shown to be violated.

10 pages, LaTex

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• Universality of Quantum Entropy for Extreme Black Holes
• Thermal Fields, Entropy, and Black Holes
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• Direct $\zeta$-function approach and renormalization of one-loop stress tensors in curved spacetimes
• Finite Temperature Effects for Massive Fields in D-dimensional Rindler-like Spaces
• Euclidean Approach to the Entropy for a Scalar Field in Rindler-like Space-Times
• Quantum Correction to the Entropy of the (2+1)-Dimensional Black Hole
• Thermodynamics of scalar fields in Kerr's geometry
• Quantum Scalar Field on the Massless (2+1)-Dimensional Black Hole Background
• Ultrastatic spacetimes
• Quantum Corrections for ABGB Black Hole
• Entropy of Quantum Fields for Nonextreme Black Holes in the Extreme Limit
• Wightman Functions' Behaviour on the Event Horizon of an Extremal Reissner-Nordström Black Hole
• Entropy of Scalar Field near a Schwarzschild Black Hole Horizon
• A Bisognano-Wichmann-like Theorem in a Certain Case of a Non Bifurcate Event Horizon related to an Extreme Reissner-Nordström Black Hole