Disturbing the Black Hole

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

Optimizing entropy bounds for macroscopic systems

The universal bound on specific entropy was originally inferred from black hole thermodynamics. We here show from classical thermodynamics alone that for a system at fixed volume or fixed pressure, the ratio of entropy to nonrelativistic energy has a unique maximum $(S/E)_\mathrm{max}$. A simple argument from quantum dynamics allows one to set a model--independent upper bound on $(S/E)_\mathrm{max}$ which is usually much tighter than the universal bound. We illustrate with two examples.Comment: 13 pages, 2 figures, LaTe