Semianalytic Quasinormal Modes for Kerr black holes: A resummed WKB approach

We develop convergent semianalytic approximants for quasinormal mode (QNM) frequencies of Kerr black holes using Padé and Padé-Borel resummation of the WKB approximation. Solving for the QNM frequencies under a series expansion of the dimensionless spin a, we found that out results are highly accurate in the slow rotation regime. For large spins, we introduce a recursive method exploiting the resummed WKB structure that attains fractional accuracy of 10^-7 for the l=2, m=0 and n=0 mode at a = 0.99.