Asymptotics of Quasi-normal Modes for Multi-horizon Black Holes

The issue concerning rigorous methods recently developed in deriving the asymptotics of quasi-normal modes is revisited and applied to a generic non rotating multi-horizon black holes solution. Some examples are illustrated and the single horizon cases are also considered. As a result, the asymptotics for large angular momentum parameter is shown to depend on the difference between the maximal or Nariai black hole mass and the ordinary black hole mass. The extremal limit is also discussed and the exact evaluation of the quasi-normal frequencies related to the Nariai space-time is presented, as a consistent check of the general asymptotic formula.