Thermodynamic Features of Black Holes Dressed with Quantum Fields

TL;DR

This paper reviews the semi-classical back reaction of quantum fields on black hole thermodynamics, calculating quantum corrections to temperature and entropy for various field types, revealing positive, monotonic entropy corrections.

Contribution

It provides a self-contained analysis of semi-classical back reaction effects on black hole thermodynamics for different quantum fields, including explicit $O()$ corrections.

Findings

Entropy corrections are positive and increase with distance from the black hole.

Quantum corrections to temperature and entropy are of the same order as flat space radiation.

Solutions for conformal scalars, spinors, and gauge bosons are obtained and analyzed.

Abstract

The thermal properties of black holes in the presence of quantum fields can be revealed through solutions of the semi-classical Einstein equation. We present a brief but self-contained review of the main features of the semi-classical back reaction problem for a black hole in the microcanonical ensemble. The solutions, obtained for conformal scalars, massless spinors and U(1) gauge bosons, are used to calculate the $O(\hbar)$ corrections to the temperature and thermodynamical entropy of a Schwarzschild black hole. In each spin case considered, the entropy corrections $\Delta S(r)$, are positive definite and monotone increasing with increasing distance $r$ from the hole, and are of the same order as the naive flat space radiation entropy.