Long time black hole evaporation with bounded Hawking flux

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]