Highly damped quasinormal modes of Kerr black holes: A complete numerical investigation

We compute for the first time very highly damped quasinormal modes of the (rotating) Kerr black hole. Our numerical technique is based on a decoupling of the radial and angular equations, performed using a large-frequency expansion for the angular separation constant ${}_s{A}_{\mathrm{lm}}.$ This allows us to go much further in overtone number than ever before. We find that the real part of the quasinormal frequencies approaches a nonzero constant value which does not depend on the spin s of the perturbing field or on the angular index l: ${\omega }_R=m\varpi \mathrm{}\left(a\right).$ We numerically compute $\varpi \mathrm{}\left(a\right).$ Leading-order corrections to the asymptotic frequency are likely to be $\sim 1/{\omega }_I.$ The imaginary part grows without bound, the spacing between consecutive modes being a monotonic function of a.