Quasinormal modes of extended gravity black holes through higher order WKB method

Black hole's quasinormal frequencies are basically the complex numbers which provide information about the relaxation of perturbations and depend on the characteristics of the spacetime and types of perturbations. In this paper, we evaluate the spectrum of the quasinormal modes of Hayward black hole in Einstein-Gauss-Bonnet gravity, Hayward black hole in anti-de Sitter space (AdS) spacetime, and 4-dimensional black hole in Einstein-Lovelock gravity. By utilizing the 6th-order WKB resonance technique, we examine the quasinormal modes frequencies ω by shifting the charge parameter Q (it is also identified with the cosmological constant), circular harmonic index l, and mass of scalar field m. We observe that 6th-order WKB method gives quite high accuracy when the multipole number l is larger than the overtone n. We observe that real and imaginary components of the quasinormal modes are not linear functions similar to Reisnner-Nordström-AdS. For large values of charge, quasinormal ringing becomes slower to settle down to thermal equilibrium and hence the frequency of the oscillation becomes smaller.