Quantum toy model for black-hole back-reaction

TL;DR

This paper introduces a quantum toy model for black hole evaporation that demonstrates how Hawking radiation causes the horizon to shrink through momentum balance, affecting heat capacity and entropy.

Contribution

It presents a simplified quantum field theoretical model showing black hole back-reaction driven by momentum, not energy conservation, and explores its thermodynamic implications.

Findings

Horizon shrinks due to momentum back-reaction

Effective heat capacity can be positive or negative

Entropy variation depends on model parameters

Abstract

We propose a simple quantum field theoretical toy model for black hole evaporation and study the back-reaction of Hawking radiation onto the classical background. It turns out that the horizon is also ``pushed back'' in this situation (i.e., the interior region shrinks) but this back-reaction is not caused by energy conservation but by momentum balance. The effective heat capacity and the induced entropy variation can have both signs -- depending on the parameters of the model. PACS: 04.62.+v, 04.70.Dy.