Long time black hole evaporation with bounded Hawkingflux

Abstract

The long time behaviour of an evaporating black hole presents achallenge to theoretical physics and touches relevant conceptualissues of quantum gravity, such as the information paradox.There are basically two strategies: top-down, i.e., constructingfirst a full quantum theory of gravity and discussing black holeevaporation as a particular application thereof, and bottom-up,i.e., sidestepping the difficulties inherent to the formerapproach by invoking `reasonable' ad hoc assumptions. Exploiting the fact that the Schwarzschild black hole can bedescribed by means of an effective theory in 2D, a particulardilaton gravity model, the latter route is pursued. A crucialtechnical ingredient is Izawa's result on consistentdeformations of 2D BF theory, while the most relevant physicalassumption is boundedness of the asymptotic matter flux duringthe whole evaporation process. Together with making technicalassumptions which can be relaxed, the dynamics of theevaporating black hole is described by means of consistentdeformations of the underlying gauge symmetries with only oneimportant deformation parameter. An attractor solution, theend-point of the evaporation process, is found. Its metric isflat. However, the behaviour of the dilaton field (whichcorresponds to the surface area) is non-trivial: it is arguedthat during the final flicker a first-order phase transitionoccurs from a linear to a constant dilaton vacuum. Consequently,a shock wave is emitted as a final `thunderbolt' with a totalenergy of a fraction of the Planck mass. Relations toultrarelativistic boosts are pointed out. Another fraction ofthe Planck mass may reside in a cold remnant. The physical discussion addresses the lifetime, the specificheat, the Carter–Penrose diagram, the information paradox andcosmological implications. The phenomenon of `dilatonevaporation' to a constant dilaton vacuum might be of relevancealso for higher dimensional scalar tensor theories.