The Semi-Classical Back Reaction to Black Hole Evaporation

TL;DR

This paper analyzes the semi-classical back reaction in black hole evaporation, confirming that black hole mass decreases following Hawking's law and particles are emitted thermally at a temperature inversely proportional to the black hole mass.

Contribution

It provides a detailed proof that the semi-classical back reaction leads to mass loss consistent with Hawking's law and confirms the thermal nature of emitted particles.

Findings

Black hole mass decreases as per Hawking's law.

Particles are emitted with a thermal spectrum.

The temperature of emission is inversely proportional to black hole mass.

Abstract

The semi-classical back reaction to black hole evaporation (wherein the renormalized energy momentum tensor is taken as source of Einstein's equations) is analyzed in detail. It is proven that the mass of a Schwarzshild black hole decreases according to Hawking's law $dM/dt = - C/ M^2$ where $C$ is a constant of order one and that the particles are emitted with a thermal spectrum at temperature $1/8\pi M(t)$.