ONE-LOOP QUANTUM CORRECTIONS TO THE ENTROPY FOR A 4-DIMENSIONAL ETERNAL BLACK HOLE

TL;DR

This paper calculates the first quantum corrections to the entropy of a 4D eternal black hole at one-loop level, revealing divergence cancellations at the Hawking temperature and providing insights into quantum effects on black hole thermodynamics.

Contribution

It introduces a method using conformal techniques and the optical metric to compute quantum corrections to black hole entropy at one-loop level in four dimensions.

Findings

Quantum corrections include quadratic, logarithmic, and finite parts.

Divergences at the horizon cancel at the Hawking temperature.

Provides insights into quantum effects on black hole thermodynamics.

Abstract

The first quantum corrections to the free energy for an eternal 4-dimensional 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. The quadratic and logarithmic divergences as well as a finite part associated with the first quantum correction to the entropy are obtained at a generic temperature. It is argued that, at the Hawking temperature, the horizon divergences of the internal energy should cancel. Some comments on the divergences of the entropy are also presented.