Analytic study of rotating black-hole quasinormal modes

A Bohr-Sommerfeld equation is derived for the highly damped quasinormal mode frequencies ω(n1) of rotating black holes. It may be written as 2∫C(pr+ip0)dr=(n+1/2)h, where pr is the canonical momentum conjugate to the radial coordinate r along a null geodesic of energy ω and angular momentum m, p0=O(ω0), and the contour C connects two complex turning points of pr. The solutions are ω(n)=-mω-i(+nδ), where {ω,δ} >0 are functions of the black-hole parameters alone. Some physical implications are discussed.