Analytic study of rotating black-hole quasinormal modes

A Bohr-Sommerfeld equation is derived for the highly damped quasinormal mode frequencies omega(n >> 1) of rotating black holes. It may be written as 2 integral(C)(p(r)+ip(0))dr=(n+1/2)h, where p(r) is the canonical momentum conjugate to the radial coordinate r along a null geodesic of energy h omega and angular momentum hm, p(0)=O(omega(0)), and the contour C connects two complex turning points of p(r). The solutions are omega(n)=-m omega boolean AND-i(phi boolean AND+n delta boolean AND), where {omega boolean AND,delta boolean AND}> 0 are functions of the black-hole parameters alone. Some physical implications are discussed.