Quasinormal resonances of rapidly-spinning Kerr black holes and the universal relaxation bound - Shahar Hod (Elsevier, 2021)
The universal relaxation bound suggests that the relaxation times of perturbed thermodynamical systems is bounded from below by the simple time-times-temperature (TTT) quantum relation τ×T≥ħπ. It is known that some perturbation modes of near-extremal Kerr black holes in the regime MTBH/ħ≪m−2 are characterized by normalized relaxation times πτ×TBH/ħ which, in the approach to the limit MTBH/ħ→0, make infinitely many oscillations with a tiny constant amplitude around 1 and therefore cannot be used directly to verify the validity of the TTT bound in the entire parameter space of the black-hole spacetime (Here {TBH,M} are respectively the Bekenstein-Hawking temperature and the mass of the black hole, and m is the azimuthal harmonic index of the linearized perturbation mode). In the present compact paper we explicitly prove that all rapidly-spinning Kerr black holes respect the TTT relaxation bound. In particular, using analytical techniques, it is proved that all black-hole perturbation modes in the complementary regime m−1≪MTBH/ħ≪1 are characterized by relaxation times with the simple dimensionless property πτ×TBH/ħ≥1.