On the branching of the quasinormal resonances of near-extremal Kerr black holes
The Ruppin Academic Center, Emeq Hefer, 40250, Israel
2 The Hadassah Institute, Jerusalem, 91010, Israel
* e-mail: firstname.lastname@example.org
Accepted: 19 October 2015
Published online: 2 November 2015
It has recently been shown by Yang et al. (Phys Rev D 87:041502(R), 2013a; Phys Rev D 88:044047, 2013b) that rotating Kerr black holes are characterized by two distinct sets of quasinormal resonances. These two families of quasinormal resonances display qualitatively different asymptotic behaviors in the extremal () black-hole limit: the zero-damping modes are characterized by relaxation times which tend to infinity in the extremal black-hole limit ( as ), whereas the damped modes (DMs) are characterized by non-zero damping rates ( finite-values as ). In this paper we refute the claim made by Yang et al. that co-rotating DMs of near-extremal black holes are restricted to the limited range , where is the dimensionless ratio between the azimuthal harmonic index m and the spheroidal harmonic index l of the perturbation mode. In particular, we use an analytical formula originally derived by Detweiler in order to prove the existence of DMs (damped quasinormal resonances which are characterized by finite values in the limit) of near-extremal black holes in the regime, the regime which was claimed by Yang et al. not to contain DMs. We show that these co-rotating DMs (in the regime ) are expected to characterize the resonance spectra of rapidly rotating (near-extremal) black holes with .
© SIF and Springer-Verlag Berlin Heidelberg, 2015