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Probing quantum anomaly corrections on black hole physics through chaos

Yu-Sen An, Wei-Hao Zhang

TL;DR

The paper investigates how quantum conformal anomaly corrections modify chaotic particle dynamics around black holes. It derives an anomaly-corrected black hole metric and analyzes chaos using two probes: Poincaré sections and Lyapunov exponents. Across two dynamical setups (neutral particles in a harmonic potential and charged particles in a radial electric field), it finds that the conformal anomaly generally enhances chaos near the horizon while preserving the near-horizon chaos bound. The results point to potential observational signatures in gravitational waves from EMRIs and motivate future work connecting chaos to phase transitions and GW detection prospects.

Abstract

The black hole horizon can induce chaotic motion of particles around the black hole. The original integrable motion of particles can transit to the chaotic motion when approaching black hole horizon. In this work, we consider the black hole background where quantum conformal anomaly correction is taken into account. We use Poincare section and Lyapunov exponent as representative probes to illustrate chaos. We investigate the effect of anomaly coefficient on the chaos of particles and for both probes, we find that quantum anomaly generally enhances the chaos of particle motions. As the chaotic orbits of particles can leave an imprint on the gravitational wave signals of the extreme mass ratio inspirals, our results pave the way to detect conformal anomaly effect in actual observations.

Probing quantum anomaly corrections on black hole physics through chaos

TL;DR

The paper investigates how quantum conformal anomaly corrections modify chaotic particle dynamics around black holes. It derives an anomaly-corrected black hole metric and analyzes chaos using two probes: Poincaré sections and Lyapunov exponents. Across two dynamical setups (neutral particles in a harmonic potential and charged particles in a radial electric field), it finds that the conformal anomaly generally enhances chaos near the horizon while preserving the near-horizon chaos bound. The results point to potential observational signatures in gravitational waves from EMRIs and motivate future work connecting chaos to phase transitions and GW detection prospects.

Abstract

The black hole horizon can induce chaotic motion of particles around the black hole. The original integrable motion of particles can transit to the chaotic motion when approaching black hole horizon. In this work, we consider the black hole background where quantum conformal anomaly correction is taken into account. We use Poincare section and Lyapunov exponent as representative probes to illustrate chaos. We investigate the effect of anomaly coefficient on the chaos of particles and for both probes, we find that quantum anomaly generally enhances the chaos of particle motions. As the chaotic orbits of particles can leave an imprint on the gravitational wave signals of the extreme mass ratio inspirals, our results pave the way to detect conformal anomaly effect in actual observations.
Paper Structure (5 sections, 35 equations, 3 figures)

This paper contains 5 sections, 35 equations, 3 figures.

Table of Contents

  1. Introduction:
  2. Black hole with conformal anomaly correction:
  3. Poincare section of conformal anomaly corrected black hole:
  4. Lyapunov exponent of conformal anomaly corrected black hole:
  5. Conclusion and Discussion:

Figures (3)

  • Figure 1: The change of Poincare section of massive particles for $\alpha_{c}=0.01$. We increase energy from left to right, as energy increases, the Poincare section is distorted and finally transits from regular KAM tori to irregular scattered points, which means that the particle motion becomes chaotic.
  • Figure 2: The change of Poincare section of massive particles for $E=60$ and different $\alpha_{c}$, as anomaly $\alpha_{c}$ increase, the Poincare section becomes distorted and irregular which means that the particle motion becomes more chaotic.
  • Figure 3: The relation between Lyapunov exponent and conformal anomaly where $M=1$ and $Q_{e}=0.5$ and charge to mass ratio is chosen to be $e/m=30,50,100$ respectively. We also plot the $\kappa^{2}$ in dashed line for reference.