Quasinormal spectrum of $(2+1)$-dimensional asymptotically flat, dS and AdS black holes

Abstract: While $(2+1)$-dimensional black holes in the Einstein theory allow for only the anti-de Sitter asymptotic, when the higher curvature correction is tuned on, the asymptotically flat, de Sitter and anti-de Sitter cases are included. Here we propose first comprehensive study of the stability and quasinormal spectra of the scalar field perturbations around such black holes with all three asymptotics. Calculations of the frequencies are fulfilled with the help of the 6th order WKB method with Pade approximants, Bernstein polynomial method and time-domain integration. Results obtained by all three methods are in a very good agreement in their common range of applicability. When the multipole moment $k$ is equal to zero, the purely imaginary, i.e. non-oscillatory, modes dominate in the spectrum for all types of the asymptotic behavior, while the spectrum at higher $k$ resembles that in four-dimensional spacetime with the corresponding asymptotic.