Quasinormal frequencies of self-dual black holes

Abstract

One simplified black hole model constructed from a semiclassical analysis of loop quantum gravity (LQG) is called the self-dual black hole. This black hole solution depends on a free dimensionless parameter $P$ known as the polymeric parameter and also on the ${a}_{0}$ area related to the minimum area gap of LQG. In the limit of $P$ and ${a}_{0}$ going to zero, the usual Schwarzschild solution is recovered. Here we investigate the quasinormal modes (QNMs) of massless scalar perturbations in the self-dual black hole background. We compute the QN frequencies using the sixth-order WKB approximation method and compare them with numerical solutions of the Regge-Wheeler equation. Our results show that, as the parameter $P$ grows, the real part of the QN frequencies suffers an initial increase and then starts to decrease while the magnitude of the imaginary one decreases for fixed area gap ${a}_{0}$. This particular feature means that the damping of scalar perturbations in the self-dual black hole spacetimes is slower, and the oscillations are faster or slower according to the value of $P$.