Imprints of topological thermodynamics on black hole dynamics

By employing Duan’s topological method, we can classify critical points based on their topological charge as Q = ± 1 , 0 . Previous work [Wei et al., PRD 105, 104003 (2022)] investigate two typical anti-de Sitter (AdS) black hole: Reissner-Nordström (RN) case (with only one critical point Q = − 1 ) and Born–Infeld (BI) case (with two critical points Q = ± 1 ). In this work, we first find that all three types of critical points exhibit in quantum anomalous black holes for 4-D spacetime. We then compute the quasinormal modes of massless scalar perturbations near these critical points, and find that both oscillation frequency and damping rate increase with black hole radii at the critical temperature. Besides such common behavior, though the Q = + 1 , 0 cases do not have a discernible pattern due to few samples, the Q = − 1 case shows very similar dynamical characteristics across all three black hole solutions, which implies a non-trivial connection between topological thermodynamics and dynamics.