Quantum field theory with boundary conditions at the horizons

Abstract

A procedure to derive a unitary evolution law for a quantised black hole has been proposed by the author. The proposal implies several assumptions, which seem almost unavoidable to this author. We start off with the question how to describe the energy eigenstates of a black hole. The background metric required for this cannot be the Vaidya metric let alone the metric proposed by Hawking, who included the effect of the final evaporation of the black hole. This however leads to the formation if firewalls at both the future and the past event horizon, unless one anticipates the effects that the firewalls have. These effects can be handled as new boundary conditions at the horizons, describing the flow of the participating particles. It is subsequently explained how these boundary conditions must involve the antipodes of the outside world. Imposing unitarity and continuity then automatically leads to a unique, unitary evolution operator. We exhibit the resulting, quite coherent picture.