Characterising the Most Rapidly Rotating AdS$_5$-Kerr Black Holes

Classical Censorship permits AdS$_5$-Kerr black holes with arbitrarily large angular momenta per unit mass, which does not seem reasonable from a holographic point of view. However, it has been shown that, when these black holes are embedded in string theory, their angular momentum per unit mass is in fact bounded by $2\sqrt{2}L$, where $L$ is the asymptotic curvature scale. One might suppose that the most rapidly rotating AdS$_5$-Kerr black holes, with angular momentum per unit mass close to this bound, might be unstable, for example, to a superradiant instability. We show that this is not always true: there is a small domain in the AdS$_5$-Kerr parameter space corresponding to black holes which are stable against superradiance and yet nearly saturate the stringy bound.