In conventional field theories, the emission of Hawking radiation in the
background of a collapsing star requires transplanckian energy fluctuations.
These fluctuations are encoded in the weak values of the energy-momentum
operator constructed from matrix elements between both -in and -out states. It
is argued that taming of these weak values by back-reaction may lead to
geometrical backgrounds which are also build from weak values of the
gravitational field operators. This leads to different causal histories of the
black hole as reconstructed by observers crossing the horizon at different
times but reduces, in accordance with the equivalence principle, to the
classical description of the collapse for the proper history of the star as
recorded by an observer comoving with it. For observers never crossing the
horizon, the evaporation would be interpreted within a topologically trivial
``achronon geometry" void of horizon and singularity: after the initial
ignition of the radiation from pair creation out of the vacuum of the
collapsing star of mass M, as in the conventional theory, the source of the
thermal radiation would shift gradually to the star itself in a time at least
of order 4Mln2M. The burning of the star could be consistent with a quantum
unitary evolution along the lines suggested by 't Hooft. A provisional formal
expression of general black hole complementarity is proposed and its possible
relevance for testing features of a theory of quantum gravity is suggested.Comment: presented at the Oskar Klein Centenary Symposium (September 1994); 29
pages, phyzzx, no figure
