Abstract
We study the stability of odd-dimensional rotating black holes with equal
angular momenta by performing an expansion in the inverse of the number of
dimensions D. Universality at large D allows us to calculate analytically the
complex frequency of quasinormal modes to leading order in the expansion. We
identify the onset of non-axisymmetric, bar-mode instabilities at a specific
finite rotation, and axisymmetric instabilities at larger rotation. The former
occur at the threshold where the modes become superradiant. Our results fully
confirm the picture found in numerical studies, with good overall quantitative
agreement. We extend the analysis to the same class of black holes in
Anti-deSitter space, and find the same qualitative features. We also discuss
the appearance at high frequencies of the universal set of (stable) quasinormal
modes.
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