Energy, Temperature, and Entropy of Black Holes Dressed with Quantum Fields

TL;DR

This paper investigates how quantum fields alter the fundamental thermodynamic relations of Schwarzschild black holes, revealing surprising corrections to the classical Bekenstein-Hawking entropy-energy-temperature relations.

Contribution

It provides new insights into the modifications of black hole thermodynamics caused by quantum field effects within semi-classical gravity, specifically for uncharged spherical black holes.

Findings

Quantum fields induce corrections to Bekenstein-Hawking relations.

The corrections reveal unexpected features in black hole entropy and energy.

Results are derived within semi-classical quantum field theory in curved spacetime.

Abstract

A deeper understanding of the thermal properties of black holes than we presently have depends to a large degree on obtaining a firmer grasp of the properties of the entropy. For such an understanding we must at least know the basic relations among entropy, energy, and temperature of a black hole in thermal equilibrium with quantized matter fields. Limiting attention to spherical, uncharged (``Schwarzschild") holes, we will find that the basic Bekenstein-Hawking relations have to be generalized when the hole is dressed by quantum fields. Though this fact is not surprising, the corrections contain surprises and are very instructive. My purpose here is to discuss several aspects of this problem and to display some concrete results within the framework of the semi-classical theory of quantum fields in curved spacetime.