  Certain AdS black holes are "fragile", in the sense that, if they are
deformed excessively, they become unstable to a fundamental non-perturbative
stringy effect analogous to Schwinger pair-production [of branes].
Near-extremal topologically spherical AdS-Kerr black holes, which are natural
candidates for string-theoretic models of the very rapidly rotating black holes
that have actually been observed to exist, do represent a very drastic
deformation of the AdS-Schwarzschild geometry. One therefore has strong reason
to fear that these objects might be "fragile", which in turn could mean that
asymptotically flat rapidly rotating black holes might be fragile in string
theory. Here we show that this does not happen: despite the severe deformation
implied by near-extremal angular momenta, brane pair production around
topologically spherical AdS-Kerr black holes is always suppressed.
