The Highly Damped Quasinormal Modes of Extremal Reissner-Nordström and Reissner-Nordström-de Sitter Black Holes

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We analyze in detail the highly damped quasinormal modes of D-dimensional extremal Reissner-Nordstrom and Reissner-Nordstrom-de Sitter black holes. We only consider the extremal case where the event horizon and the Cauchy inner horizon coincide. We show that, even though the topology of the Stokes/anti-Stokes lines in the extremal case is different than the non-extremal case, the highly damped quasinormal mode frequencies of extremal black holes match exactly with the extremal limit of the non-extremal black hole quasinormal mode frequencies.