Highly damped quasinormal modes of generic single-horizon black holes

We calculate analytically the highly damped quasinormal mode spectra of generic single-horizon black holes using the rigorous WKB techniques of Andersson and Howls ( 2004 Class. Quantum Grav. 21 1623 ). We thereby provide a firm foundation for previous analysis, and point out some of their possible limitations. The numerical coefficient in the real part of the highly damped frequency is generically determined by the behaviour of coupling of the perturbation to the gravitational field near the origin, as expressed in tortoise coordinates. This fact makes it difficult to understand how the famous ln(3) could be related to the quantum gravitational microstates near the horizon.