Quasinormal Spectrum of ( 2 + 1 ) $(2+1)$ -Dimensional Asymptotically Flat, dS and AdS Black Holes

While $(2+1)$-dimensional black holes in the Einstein theory allow for only the anti-de Sitter (AdS) asymptotic, when the higher curvature correction is tuned on, the asymptotically flat, de Sitter, and AdS cases are included. Here, a detailed study of the stability and quasinormal spectra of the scalar field perturbations around such black holes with all three asymptotics is proposed. Calculations of the frequencies are fulfilled with the help of the 6th order Wentzel–Kramers–Brillouin (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.