How the Change in Horizon Area Drives Black Hole Evaporation

TL;DR

This paper derives a new formula for black hole radiation that accounts for changes in horizon area, linking quantum emission probabilities to horizon thermodynamics and extending to cosmological horizons.

Contribution

It introduces a derivation of black hole radiation based on horizon area dynamics, improving upon Hawking's temperature-based approach and connecting to classical thermodynamics.

Findings

Emission probability proportional to exponential of area decrease

Inclusion of specific heat effects in black hole radiation

Applicability to cosmological and acceleration horizons

Abstract

We rephrase the derivation of black hole radiation so as to take into account, at the level of transition amplitudes, the change of the geometry induced by the emission process. This enlarged description reveals that the dynamical variables which govern the emission are the horizon area and its conjugate time variable. Their conjugation is established through the boundary term at the horizon which must be added to the canonical action of general relativity in order to obtain a well defined action principle when the area varies. These coordinates have already been used by Teitelboim and collaborators to compute the partition function of a black hole. We use them to show that the probability to emit a particle is given by $e^{- \Delta A/4}$ where $\Delta A$ is the decrease in horizon area induced by the emission. This expression improves Hawking result which is governed by a temperature (given by the surface gravity) in that the specific heat of the black hole is no longer neglected. The present derivation of quantum black hole radiation is based on the same principles which are used to derive the first law of classical black hole thermodynamics. Moreover it also applies to quantum processes associated with cosmological or acceleration horizons. These two results indicate that not only black holes but all event horizons possess an entropy which governs processes according to quantum statistical thermodynamics.