We motivate through a detailed analysis of the Hawking radiation in a
Schwarzschild background a scheme in accordance with quantum unitarity. In this
scheme the semi-classical approximation of the unitary quantum - horizonless -
black hole S-matrix leads to the conventional description of the Hawking
radiation from a classical black hole endowed with an event horizon. Unitarity
is borne out by the detailed exclusive S-matrix amplitudes. There, the fixing
of generic out-states, in addition to the in-state, yields in asymptotic
Minkowski space-time saddle-point contributions which are dominated by
Planckian metric fluctuations when approaching the Schwarzschild radius. We
argue that these prevent the corresponding macroscopic "exclusive backgrounds"
to develop an event horizon. However, if no out-state is selected, a distinct
saddle-point geometry can be defined, in which Planckian fluctuations are
tamed. Such "inclusive background" presents an event horizon and constitutes a
coarse-grained average over the aforementioned exclusive ones. The classical
event horizon appears as a coarse-grained structure, sustaining the
thermodynamic significance of the Bekenstein-Hawking entropy. This is
reminiscent of the tentative fuzzball description of extremal black holes: the
role of microstates is played here by a complete set of out-states. Although
the computations of unitary amplitudes would require a detailed theory of
quantum gravity, the proposed scheme itself, which appeals to the metric
description of gravity only in the vicinity of stationary points, does not.Comment: 29 pages, 4 figures. Typos corrected. Two footnotes added (footnotes
3 and 5
