Long time black hole evaporation with bounded Hawking flux

The long time behavior of an evaporating black hole presents a challenge to theoretical physics and touches relevant conceptual issues of quantum gravity, such as the information paradox. There are basically two strategies: top-down, i.e., to construct first a full quantum theory of gravity and to discuss black hole evaporation as a particular application thereof, and bottom-up, i.e., to sidestep the difficulties inherent to the former approach by invoking “reasonable” ad-hoc assumptions. Exploiting the fact that the Schwarzschild black hole can be described by means of an effective theory in 2D, a particular dilaton gravity model, the latter route is pursued. 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. Together with technical assumptions which can be relaxed, the dynamics of the evaporating black hole is described by means of consistent deformations of the underlying gauge symmetries with only one important deformation parameter. An attractor solution, the endpoint of the evaporation process, is found. Its metric is flat. However, the behavior of the dilaton field (which corresponds to the surface area) is nontrivial: it is argued that during the final flicker a first order phase transition occurs from a linear to a constant dilaton vacuum. Consequently, a shock wave is emitted as a final “thunderbolt” with a total energy of a fraction of the Planck mass. Relations to ultrarelativistic boosts are pointed out. Another fraction of the Planck mass may reside in a cold remnant. The physical discussion addresses the life time, the specific heat, the Carter-Penrose diagram, the information paradox and cosmological implications. The phenomenon of “dilaton evaporation” to a constant dilaton vacuum might be of relevance also for higherdimensional scalar tensor theories. e-mail: [email protected]