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We study analytically the highly damped quasinormal modes of Kerr black holesin the small angular momentum limit. To check the previous analyticcalculations in the literature, which use a combination of radial and tortoisecoordinates, we reproduce all the results using the radial coordinate only.According to the earlier calculations, the real part of the highly dampedquasinormal mode frequency of Kerr black holes approaches zero in the limitwhere the angular momentum goes to zero. This result is not consistent with theSchwarzschild limit where the real part of the highly damped quasinormal modefrequency is equal to c^3 ln(3)/(8 pi G M). In this paper, our calculationssuggest that the highly damped quasinormal modes of Kerr black holes in thezero angular momentum limit make a continuous transition from the Kerr value tothe Schwarzschild value. We explore the nature of this transition using acombination of analytical and numerical techniques. Finally, we calculate thehighly damped quasinormal modes of the extremal case in which the topology ofStokes/anti-Stokes lines takes a different form.

Asymptotic Spectrum of Kerr Black Holes in the Small Angular Momentum Limit