We study the universal nature of the product of the entropies of all horizons
of charged rotating black holes. We argue, by examining further explicit
examples, that when the maximum number of rotations and/or charges are turned
on, the entropy product is expressed in terms of angular momentum and/or
charges only, which are quantized. (In the case of gauged supergravities, the
entropy product depends on the gauge-coupling constant also.) In two-derivative
gravities, the notion of the "maximum number" of charges can be defined as
being sufficiently many non-zero charges that the Reissner-Nordstrom black hole
arises under an appropriate specialisation of the charges. (The definition can
be relaxed somewhat in charged AdS black holes in D≥6.) In
higher-derivative gravity, we use the charged rotating black hole in
Weyl-Maxwell gravity as an example for which the entropy product is still
quantized, but it is expressed in terms of the angular momentum only, with no
dependence on the charge. This suggests that the notion of maximum charges in
higher-derivative gravities requires further understanding.Comment: References added. 24 page
