Highly damped Quasi-Normal Modes of a Loop Quantum Black Hole

Abstract

We compute asymptotic Quasi-Normal Mode (QNM) frequencies -- i.e. frequencies with a very large Imaginary part -- of a Loop Quantum Gravity inspired Black Hole. The deformations from the Schwarzschild Black Hole are encoded via two parameters: the minimal area gap $a_0$ and the polymeric deformation parameter $P$. In this study, we focus on the effect of the latter one, $P$, on the highly-damped part of QNM spectra. We consider both spin 0 and spin 2 test-field perturbations on the Black Hole as proper gravitational perturbations cannot be performed on an effective model. We use an analytical method of computation of QNMs referred to as the monodromy technique, which allows us to compute the asymptotic behaviour of QNMs. We found interesting oscillating behaviour in both the Real part and the Imaginary part of the QNMs, where the oscillation period varies with the polymeric deformation parameter $P$. We compare these analytical predictions to numerical results obtained thanks to the Continued fraction method. Even though the latter does not converge for QNMs with a very large Imaginary part, the numerical results are in rather good agreement with the monodromy prediction.