One-loop Quantum Corrections to the Entropy for an Extremal Reissner-Nordstr\"om Black Hole

TL;DR

This paper calculates the first quantum corrections to the entropy of an extremal Reissner-Nordström black hole, revealing divergences and violations of the area law at one-loop level.

Contribution

It introduces a method using conformal techniques and optical metrics to evaluate quantum entropy corrections for extremal black holes.

Findings

Identifies a leading cubic divergence at the horizon

Finds additional divergences from optical manifold singularities

Demonstrates violation of the classical area law

Abstract

The first quantum corrections to the entropy for an eternal 4-dimensional extremal Reissner-Nordstr\"om 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.