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There has been some recent speculation that a connection may exist betweenthe quasinormal-mode spectra of highly damped black holes and the fundamentaltheory of quantum gravity. This notion follows from a conjecture by Hod thatthe real part of the highly damped mode frequencies can be used to calibratethe semi-classical level spacing in the black hole quantum area spectrum.However, even if the level spacing can be fixed in this manner, it stillremains unclear whether this implies a physically significant "duality" ormerely a numerical coincidence. This tapestry of ideas serves as the motivationfor the current paper. We utilize the "monodromy approach" to calculate thequasinormal-mode spectra for a generic class of black holes in two-dimensionaldilatonic gravity. Our results agree with the prior literature whenever adirect comparison is possible and provide the analysis of a much more diverseclass of black hole models than previously considered.Comment: 20 pages, in Revtex; (v2) some new references and minor changes to  the text; (v3) some clarity added to Introduction and new referenc

Quasinormal modes for single horizon black holes in generic 2D dilaton gravity