Songbai Chen and Jiliang Jing calculate a formula that is perhaps the single most general existing generalization of our formula with Andy Neitzke describing the asymptotic, highly-damped scalar quasinormal modes of the Reissner-Nordström black hole. Their setup involves a scalar field coupled to the Gibbons-Maeda dilaton spacetime with a general coupling.
The contours in the monodromy method immitate our contours in the Reissner-Nordström case. Also their result is similar and it involves the exponentials that depend both on the Hawking temperature as well as the temperature of the inner horizon. In their case, there is also an additional square-root dependence on the coupling "xi" of the scalar. This dependence is another piece in (already) overwhelming evidence that "log(3)" is not universal but depends on many couplings and other details. An entertaining feature is that the Reissner-Nordström result is reproduced for "xi=91/18".
I am actually a bit confused by this number. Don't you reproduce the same result for "xi=-5/18", among many other choices? Why is it exactly "91/18" that was chosen?
More generally, I am still convinced that a future understanding of general relativity and physics of black holes and horizons, including thermodynamics and the (absence of) the information loss paradoxes will involve much more complexification, analytical continuation, and computations in unphysical regions of the parameter space than the current descriptions. The continuation of physics into complex (and other unphysical) values of the parameters (such as the spacetime coordinates) is relevant and legitimate in quantum gravity much like it is relevant in quantum field theory. However, in the case of quantum gravity, there are many ways how the continuation may be done and there are many subtleties that one must be careful about. In my opinion, it means that analytical continuation will be an even more important and bulky portion of our future understanding of quantum gravity than the role they play in quantum field theory. Although these particular quasinormal calculations only depend on the low-energy effective action, I may imagine that various sophisticated and diverse ways to analytically continue physics to unconventional regions of the parameter space may become important for string theory itself.