Scalar quasinormal modes for 2 + 1 -dimensional Coulomb-like AdS black holes from nonlinear electrodynamics

We study the propagation of scalar fields in the background of 2 + 1 -dimensional Coulomb-like AdS black holes, and we show that such propagation is stable under Dirichlet boundary conditions. Then, we solve the Klein–Gordon equation by using the pseudospectral Chebyshev method and the Horowitz–Hubeny method, and we find the quasinormal frequencies. Mainly, we find that the quasinormal frequencies are purely imaginary for a null angular number and they are complex and purely imaginary for a non-null value of the angular number, which depend on the black hole charge, angular number and overtone number. On the other hand, the effect of the inclusion of a Coulomb-like field from nonlinear electrodynamics to general relativity for a vanishing angular number is the emergence of two branches of quasinormal frequencies in contrast with the static BTZ black hole.