Black-hole normal modes: A WKB approach. IV. Kerr black holes

Using the higher-order WKB method developed by Iyer and Will, we have computed the low-lying normal modes of Kerr black holes for both scalar and gravitational perturbations. For the gravitational modes, we compare our results to previously published numerical results. For some of these modes, we find agreement to within 1% for both the real and imaginary parts of the normal-mode frequency over a wide range of values for the rotation parameter $a$ of the black hole. For other modes, good agreement is limited to lower values of $a$. The difficulties of the method for higher values of the rotation parameter are discussed.