Quasinormal frequencies of self-dual black holes

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.