Love Numbers for Extremal Kerr Black Hole

Abstract: We perform a detailed study of the gravitational tidal Love numbers of extremal zero-temperature Kerr black holes. These coefficients are finite and exhibit the dissipative nature of these maximally spinning black holes. Upon considering the dynamical behavior of the tidal deformations of the extremal Kerr black holes, we provide explicit expressions of the Love numbers at low frequencies. Their calculation is simplified to specific formulas, which are directly derived using the Leaver-MST methods.