Quasinormal Modes of Self-Dual Loop Quantum Gravity Corrected Kerr Black Holes

Abstract

We investigate scalar quasinormal modes and ringdown signals of a rotating loop quantum gravity black hole constructed via the revised Newman--Janis algorithm. The spacetime incorporates two quantum parameters, the polymeric parameter $P$ and the minimal area parameter $a_0$, and reduces to the Kerr spacetime in the classical limit. Using the sixth-order WKB approximation and time-domain integration, we analyze the effective potential, quasinormal mode spectrum, and ringdown dynamics. The polymeric parameter $P$ systematically reduces the oscillation frequency $\mathrm{Re}(ω)$, while the spin parameter $a$ enhances it. The time-domain signals exhibit clear dependence on the multipole number $\ell$ and overtone index $n$. Our results provide a theoretical framework for understanding the effects of loop quantum gravity corrections on black hole perturbations and gravitational-wave ringdown signals.