  Based on various string theoretic constructions, and various string-inspired
generalizations thereof, there have been repeated suggestions that the areas of
black hole event horizons might be quantized in a quite specific manner, in
terms of linear combinations of square roots of positive integers. It is
important to realise that there are significant physical constraints on such
integer-based proposals when one (somewhat speculatively) attempts to extend
them outside their original extremal and supersymmetric framework.
Specifically, in their most natural and direct physical interpretations, some
of the more speculative integer-based proposals for the quantization of horizon
areas fail for the ordinary Kerr-Newman black holes in (3+1) dimensions,
essentially because the fine structure constant is not an integer. A more
baroque interpretation involves asserting the fine structure constant is the
square root of a rational number; but such a proposal has its own problems.
Insofar as one takes (3+1) general relativity (plus the usual quantization of
angular momentum and electric charge) as being paramount, the known explicitly
calculable spectra of horizon areas for the physically compelling Kerr-Newman
spacetimes indicate that some caution is called for when assessing the
universality of some of the more speculative integer-based string-inspired
proposals.
