Chaos in the near-horizon dynamics of the dyonic $\rm{AdS_4}$-Reissner-Nordstr\"{o}m black hole

TL;DR

This paper explores how chaos manifests near the horizon of dyonic AdS4-Reissner-Nordström black holes, revealing energy-dependent effects on Lyapunov exponents and phase-space structure, with implications for black hole thermodynamics and holography.

Contribution

It provides a detailed analysis of chaos in near-horizon particle dynamics, highlighting how energy and extremality influence Lyapunov exponents and phase diagrams, linking black hole thermodynamics to microscopic chaos.

Findings

Chaos is enhanced at low energy and can violate the chaos bound in extremal black holes.

At high energy, extremality suppresses chaos, leading to regular dynamics.

A direct mapping between black hole thermodynamics and chaos is established.

Abstract

We investigate the chaos in the dynamics of a probe massless particle confined by the harmonic potential near the horizon of the dyonic $\rm{AdS_4}$-Reissner-Nordstr\"om black hole. The total energy of the particle, chemical potential and magnetic field in this system serving as independently adjustable parameters tune nonlinearity and phase-space structure. By analyzing the trajectories on the Poincar\'e section and evaluating the Lyapunov exponents, we obtain the dynamical phase diagrams of the chaos and find their counteracting regulatory role: at low energy, chaos is enhanced and the Lyapunov exponent $\lambda_L$ violates its upper bound (i.e. surface gravity) in the extremal black hole limit(combined paramete $\Gamma=3$); at high energy, the same extremal limit suppresses chaos, with $\lambda_L$ dropping to zero and a regular dynamical corridor emerging along $\Gamma=3$ in the dynamical phase diagrams. These results establish a direct mapping between black hole thermodynamics and microscopic chaos, offering new insights into the AdS/QCD correspondence and nonlinear dynamics in strongly curved spacetimes.