I describe some examples in support of the conjecture that the horizon area
of a near equilibrium black hole is an adiabatic invariant. These include a
Schwarzschild black hole perturbed by quasistatic scalar fields (which may be
minimally or nonminimally coupled to curvature), a Kerr black under the
influence of scalar radiation at the superradiance treshold, and a
Reissner--Nordstr\"om black hole absorbing a charge marginally. These clarify
somewhat the conditions under which the conjecture would be true. The desired
``adiabatic theorem'' provides an important motivation for a scheme for black
hole quantization.Comment: 15 pages, LaTeX with crckapb style, to appear in ``The Black Hole
Trail'', eds. B. Bhawal and B. Iyer (Kluwer, Dordrecht 1998
