  We argue that the infinitely many gauge symmetries of string theory provide
an infinite set of conserved (gauge) quantum numbers (W-hair) which
characterise black hole states and maintain quantum coherence, even during
exotic processes like black hole evaporation/decay. We study ways of measuring
the W-hair of spherically-symmetric four-dimensional objects with event
horizons, treated as effectively two-dimensional string black holes.
Measurements can be done either through the s-wave scattering of light
particles off the string black-hole background, or through interference
experiments of Aharonov-Bohm type. We also speculate on the role of the
extended W-symmetries possessed by the topological field theories that describe
the region of space-time around a singularity.
