On the Evaporation of Black Holes in String Theory

TL;DR

This paper investigates black hole evaporation in string theory, linking quantum decay to higher-genus string amplitudes and showing the matrix model as the endpoint of evaporation in perturbation theory.

Contribution

It demonstrates that black hole decay in string theory is connected to imaginary parts in string amplitudes and confirms the matrix model as the final evaporation stage.

Findings

Imaginary parts in string amplitudes relate to black hole decay.

Matrix model limit shows no imaginary parts, indicating endpoint of evaporation.

Results are expected to extend to higher-dimensional target spaces.

Abstract

We show that, in string theory, the quantum evaporation and decay of black holes in two-dimensional target space is related to imaginary parts in higher-genus string amplitudes. These arise from the regularisation of modular infinities due to the sum over world-sheet configurations, that are known to express the instabilities of massive string states in general, and are not thermal in character. The absence of such imaginary parts in the matrix model limit confirms that the latter constitutes the final stage of the evaporation process, at least in perturbation theory. Our arguments appear to be quite generic, related only to the summation over world-sheet surfaces, and hence should also apply to higher-dimensional target spaces.