Numerical Analysis of Black Hole Evaporation

TL;DR

This paper numerically solves equations describing black hole evaporation in two-dimensional dilaton gravity, demonstrating complete evaporation in finite time and discussing boundary conditions to extend the model beyond singularities.

Contribution

It provides the first detailed numerical analysis of black hole evaporation in this model, clarifying the end state and boundary conditions for the equations.

Findings

Black holes evaporate completely in finite time.

A boundary condition can restore the system to vacuum after evaporation.

Analysis applies to scattering of fermions by extremal dilatonic black holes.

Abstract

Black hole formation/evaporation in two-dimensional dilaton gravity can be described, in the limit where the number $N$ of matter fields becomes large, by a set of second-order partial differential equations. In this paper we solve these equations numerically. It is shown that, contrary to some previous suggestions, black holes evaporate completely a finite time after formation. A boundary condition is required to evolve the system beyond the naked singularity at the evaporation endpoint. It is argued that this may be naturally chosen so as to restore the system to the vacuum. The analysis also applies to the low-energy scattering of $S$-wave fermions by four-dimensional extremal, magnetic, dilatonic black holes.