The use the monodromy technique to calculate not only the well-known zeroth order approximation of the highly-damped quasinormal frequencies - a topic previously discussed here on this blog - but also the first perturbative correction for a variety of types of perturbations of d-dimensional spherically symmetric neutral and charged black holes.
Concerning the previous literature: I don't want to mention my and Andy Neitzke's papers here because they're quite publicized, but what I want to mention is the 100-page-long paper of Jose Natario and Ricardo Schiappa that is doing a superb job in analyzing more or less all cases.
Back to Shu and Shen.
One of the topics to which they dedicate special attention is an apparent paradox that the black holes with a very tiny charge seem to have a different asymptotic behavior from the neutral black holes: the limit "q goes to 0" is not continuous. We have decided with Andy Neitzke that the resolution must be that if "q" is very small but finite, the Schwarzschild asymptotic behavior holds pretty well for a large number "n" of modes ("n" goes to infinity for "q" going to zero) but eventually the charged asymptotic behavior takes over. They are probably more detailed than Andy who described it in his paper on greybody factors even though I don't know so far what they exactly add.
As they also summarize in the last sentence of the abstract and elsewhere, they join those who confirm the viewpoint that the appearance of "ln(3)" in the quasinormal frequencies is a numerical coincidence for neutral black holes, not a general rule that could be used to support simple hypotheses about quantum gravity. I am not sure whether Lee Smolin reads this blog and whether he will again argue somewhere that loop quantum gravity can predict the correct numerical coefficient of the black hole entropy. More observant readers of this blog will know that this conjecture is safely ruled out.
Moreover, "ln(k)" for an integer value of "k" is no longer the coefficient predicted by loop quantum gravity anyway; the currently believed value is much more transcendental. See, for example, Krzysztof Meissner's paper and its 60+ followups.
