Purely imaginary polar resonances of rapidly-rotating Kerr black holes

We prove the existence of a unique family of non-oscillatory (purely-imaginary) polar quasinormal resonances of rapidly-rotating Kerr black holes. These purely imaginary resonances can be expressed in the compact form: w_n=-i2piT_{BH}*(l+1+n), where T_{BH} is the black-hole temperature, l is the spheroidal harmonic index of the mode, and n=0,1,2,… is the resonance parameter. It is shown that our analytical results for the black-hole resonance spectrum agree with new numerical data that recently appeared in the literature.