Imprints of Topological Thermodynamics on Black Hole Dynamics

Abstract: By employing Duan's topological method, we classify critical points by their topological charge Q = +/-1 or 0. Previous work (Wei et al., Phys. Rev. D 105, 104003, 2022) investigated two typical anti-de Sitter (AdS) black holes: the Reissner-Nordstroem (RN) case (with only one critical point Q = -1) and the Born-Infeld (BI) case (with two critical points Q = +/-1). In this work, we first find that all three types of critical points appear in quantum anomalous black holes for 4D spacetime. We then compute the quasinormal modes of massless scalar perturbations near these critical points and find that both the oscillation frequency and damping rate increase with the black hole radius at the critical temperature. Besides such common behavior, although the Q = +1 and Q = 0 cases do not show a discernible pattern due to the limited number of samples, the Q = -1 case exhibits very similar dynamical characteristics across all three black hole solutions, implying a nontrivial connection between topological thermodynamics and dynamics.