  In previous papers we have shown how strings in a two-dimensional target
space reconcile quantum mechanics with general relativity, thanks to an
infinite set of conserved quantum numbers, ``W-hair'', associated with
topological soliton-like states. In this paper we extend these arguments to
four dimensions, by considering explicitly the case of string black holes with
radial symmetry. The key infinite-dimensional W-symmetry is associated with the
$\frac{SU(1,1)}{U(1)}$ coset structure of the dilaton-graviton sector that is a
model-independent feature of spherically symmetric four-dimensional strings.
Arguments are also given that the enormous number of string {\it discrete
(topological)} states account for the maintenance of quantum coherence during
the (non-thermal) stringy evaporation process, as well as quenching the large
Hawking-Bekenstein entropy associated with the black hole. Defining the latter
as the measure of the loss of information for an observer at infinity, who -
ignoring the higher string quantum numbers - keeps track only of the classical
mass,angular momentum and charge of the black hole, one recovers the familiar a
quadratic dependence on the black-hole mass by simple counting arguments on the
asymptotic density of string states in a linear-dilaton background.
