  We have argued previously, based on the analysis of two-dimensional stringy
black holes, that information in stringy versions of four-dimensional
Schwarzschild black holes (whose singular regions are represented by
appropriate Wess-Zumino-Witten models) is retained by quantum $W$-symmetries
when the horizon area is not preserved due to Hawking radiation. It is key that
the exactly-marginal conformal world-sheet operator representing a massless
stringy particle interacting with the black hole requires a contribution from
$W_\infty$ generators in its vertex function. The latter correspond to
delocalised, non-propagating, string excitations that guarantee the transfer of
information between the string black hole and external particles. When
infalling matter crosses the horizon, these topological states are excited via
a process: (Stringy black hole) + infalling matter $\rightarrow $ (Stringy
black hole)$^\star$, where the black hole is viewed as a stringy state with a
specific configuration of $W_\infty$ charges that are conserved. Hawking
radiation is then the reverse process, with conservation of the $W_\infty$
charges retaining information. The Hawking radiation spectrum near the horizon
of a Schwarzschild or Kerr black hole is specified by matrix elements of
higher-order currents that form a phase-space $W_{1+\infty}$ algebra. We show
that an appropriate gauging of this algebra preserves the horizon
two-dimensional area classically, as expected because the latter is a conserved
Noether charge.
