  It is well known that an asymptotically flat four-dimensional Kerr black hole
has a smaller (specific) entropy than a Schwarzschild black hole of the same
mass. We show here that the same is true if the temperature, rather than the
mass, is held fixed; and we also show that an asymptotically AdS$_5$-Kerr black
hole has a smaller specific entropy than an AdS$_5$-Schwarzschild black hole of
the same temperature, except in a negligibly small class of special examples.
The AdS$_5$-Kerr case is particularly interesting, because here the
gauge-gravity duality applies; if we further accept that there is a useful
analogy between the strongly coupled field theories dual to AdS black holes and
the best-understood example of a strongly coupled fluid (the Quark-Gluon
Plasma), then we can apply QGP theory to predict the behaviour of black hole
entropy in this case. The prediction agrees with our study of AdS$_5$-Kerr
entropy. The hope is that such results might lead ultimately to an
identification of black hole microstates.
