Quasinormal modes of generalized ABG black holes: scalar and gravitational perturbations

ABG black holes are charged regular black holes based on Einstein gravity and nonlinear electrodynamics, proposed by Ayon-Beato and Garcia. In 2005, they generalized the ABG black holes to a new class of regular black holes which have four characteristic parameters: the mass m, the electric charge q and the rest two parameters alpha and beta related with the dipole and quadrupole moment of the nonlinear electromagnetic field, respectively. In this paper, we study the quasinormal modes (QNMs) of these generalized ABG black holes for scalar and gravitational perturbations by the sixth-order WKB method. The numerical results show the generalized ABG black holes are stable and the relations between QNMs and the parameter of the perturbation fields and the parameters of the black holes are discussed. The real part and the imaginary part of the generalized ABG black holes increase as the charge increasing. Furthermore, the dependence of the QNMs on the other parameters is also illustrated and the analytical expression of the quasinormal frequency for the large multipole index is obtained.