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Imprints of Topological Thermodynamics on Black Hole Dynamics

Yue Chu, Chen-Hao Wu, Ya-Peng Hu

TL;DR

The paper investigates how topological classification of black-hole critical points, via Duan's $\\phi$-mapping, manifests in dynamical responses by analyzing massless scalar quasinormal modes (QNMs) near isothermal critical points across RN–AdS, BI–AdS, and quantum anomalous (QA) AdS black holes. It extends the topological framework to a four-dimensional QA–BH, revealing all three charges $Q \\in \\{-1,0,+1\\}$, including an isolated critical point with $Q=0$, and computes QNMs at $T_c$ to compare dynamical behavior across topological classes. A key finding is that while $Q=-1$ cases across different BHs show a strikingly similar dynamical response ( trends in $\\omega_R$ and $|\\omega_I|$ with $r_H$ and comparable slopes), the $Q=0$ and $Q=+1$ classes exhibit more pronounced topology-dependent variations. Overall, the work uncovers a thermodynamic-topology imprint on black hole dynamics, linking phase-transition topology to the dynamical fingerprints captured by QNMs and suggesting broader implications for AdS/CFT thermodynamics and perturbation theory.

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.

Imprints of Topological Thermodynamics on Black Hole Dynamics

TL;DR

The paper investigates how topological classification of black-hole critical points, via Duan's -mapping, manifests in dynamical responses by analyzing massless scalar quasinormal modes (QNMs) near isothermal critical points across RN–AdS, BI–AdS, and quantum anomalous (QA) AdS black holes. It extends the topological framework to a four-dimensional QA–BH, revealing all three charges , including an isolated critical point with , and computes QNMs at to compare dynamical behavior across topological classes. A key finding is that while cases across different BHs show a strikingly similar dynamical response ( trends in and with and comparable slopes), the and classes exhibit more pronounced topology-dependent variations. Overall, the work uncovers a thermodynamic-topology imprint on black hole dynamics, linking phase-transition topology to the dynamical fingerprints captured by QNMs and suggesting broader implications for AdS/CFT thermodynamics and perturbation theory.

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.
Paper Structure (8 sections, 19 equations, 2 figures, 5 tables)

This paper contains 8 sections, 19 equations, 2 figures, 5 tables.

Table of Contents

  1. Introduction
  2. Topological Charge of Critical Points
  3. General Framework of Topological Current Theory
  4. TOPOLOGY OF BLACK HOLE SYSTEMS
  5. The behavior of quasinormal frequencies at the critical point with different topological classification
  6. Massless Perturbations in Black Hole Spacetime
  7. The Behavior of Quasinormal Frequencies at the Critical Point
  8. Conclusion and Discussions

Figures (2)

  • Figure 1: The rainbow-colored arrows represent the vector field $n$ on a portion of the $\theta-r_h$ plane with $\alpha_c=1/16$ and $q=1$. The critical points $CP_{1}$ and $CP_{2}$ located at $(r_h-\theta)=(0.560, \pi/2)$ and $(2.046, \pi/2)$ are marked with black dots, and they are enclosed with the blue contour $C_1$ and $C_2$, respectively. The topological charge on the $CP_{1}$ (antivortex) is 1, the one on the right (vortex) is -1.
  • Figure 2: The rainbow-colored arrows represent the vector field $n$ on a portion of the $\theta-r_h$ plane for two values of $\alpha_c$. Left: setting $\alpha_c=0.124$, there are two critical points positioned very close to each other. The left-hand point (antivortex) carries a positive topological charge, whereas the right-hand point (vortex) carries a negative one. Right: setting $\alpha_c=1/8$, there are no fixed points of $n^a$, and the $CP_5$ which is also called ICP and marked by a black dot, possesses zero topological charge, as confirmed by integrating along the blue contour shown in the figure.