Long time black hole evaporation with bounded Hawking flux

TL;DR

This paper investigates the long-term evaporation of Schwarzschild black holes using a 2D dilaton gravity model, revealing an attractor endpoint with a flat metric and a phase transition in the dilaton field, possibly leaving a remnant.

Contribution

It introduces a novel analysis of black hole evaporation with bounded Hawking flux, identifying an attractor solution and a phase transition in the dilaton field during evaporation.

Findings

Identifies an attractor solution with flat metric at evaporation endpoint.

Discovers a phase transition in the dilaton field during the final evaporation stage.

Suggests the formation of a shock wave and a possible cold remnant.

Abstract

The long time behavior of an evaporating Schwarzschild black hole is studied exploiting that it can be described by an effective theory in 2D, a particular dilaton gravity model. A crucial technical ingredient is Izawa's result on consistent deformations of 2D BF theory, while the most relevant physical assumption is boundedness of the asymptotic matter flux during the whole evaporation process. An attractor solution, the endpoint of the evaporation process, is found. Its metric is flat. However, the behavior of the dilaton field is nontrivial: it is argued that during the final flicker a first order phase transition occurs from a linear to a constant dilaton vacuum, thereby emitting a shock wave with a total energy of a fraction of the Planck mass. Another fraction of the Planck mass may reside in a cold remnant. [Note: More detailed abstract in the paper]