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We analyze in detail the highly damped quasinormal modes of $D$-dimensionalextremal Reissner-Nordstr$\ddot{\rm{o}}$m andReissner-Nordstr$\ddot{\rm{o}}$m-de Sitter black holes. We only consider theextremal case where the event horizon and the Cauchy inner horizon coincide. Weshow that, even though the topology of the Stokes/anti-Stokes lines in theextremal case is different than the non-extremal case, the highly dampedquasinormal mode frequencies of extremal black holes match exactly with theextremal limit of the non-extremal black hole quasinormal mode frequencies.

The Highly Damped Quasinormal Modes of Extremal Reissner-Nordstr\"om and Reissner-Nordstr\"om-de Sitter Black Holes