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We investigate the chaotic dynamics of test particle motion around a Kerr black hole in the infra-red limit of asymptotically safe gravity. The stability of null circular geodesics is analyzed using the Lyapunov exponent. The phase-space structure is explored through Poincaré sections, revealing the transition between regular and chaotic motion for different values of the black hole spin and quantum gravity correction parameters. Chaotic behavior is further quantified using the largest Lyapunov exponent and the fast Lyapunov indicator. In addition, we apply the weighted Birkhoff average and the discrete indicator of chaotic dynamics to characterize the long-term dynamics. Our findings show that quantum gravity corrections significantly affect the stability of photon orbits and enhance chaotic features in the geodesic motion. These effects could, in principle, be probed through high-resolution measurements of the photon sphere morphology of astrophysical black holes with next-generation observational missions.
Kala et al. (Fri,) studied this question.