  There has been some recent speculation that a connection may exist between
the quasinormal-mode spectra of highly damped black holes and the fundamental
theory of quantum gravity. This notion follows from a conjecture by Hod that
the real part of the highly damped mode frequencies can be used to calibrate
the semi-classical level spacing in the black hole quantum area spectrum.
However, even if the level spacing can be fixed in this manner, it still
remains unclear whether this implies a physically significant "duality" or
merely a numerical coincidence. This tapestry of ideas serves as the motivation
for the current paper. We utilize the "monodromy approach" to calculate the
quasinormal-mode spectra for a generic class of black holes in two-dimensional
dilatonic gravity. Our results agree with the prior literature whenever a
direct comparison is possible and provide the analysis of a much more diverse
class of black hole models than previously considered.
