Abstract In a quantum theory of gravity, a renormalization group improved Kerr metric is obtained from the Kerr metric, where the Newton gravitational constant is modified as a function of the radial distance. The motion of neutral test particles in this metric is integrable. However, the dynamics of charged test particles is nonintegrable when an external asymptotically homogeneous magnetic field exists in the vicinity of the black hole. The transition from regular dynamics to chaotic dynamics is numerically traced as one or two dynamical parameters vary. From a statistical point of view, the strength of chaos is typically enhanced as both the particle energy and the magnetic field increase, but it is weakened with increasing the particle angular momentum and the black hole spin. In particular, an increase of the quantum corrected parameter weakens the extent of chaos. This is because the running Newton gravity constant effectively weakens the central gravitational attraction and results in decreasing sensitivity to initial conditions.
Lu et al. (2025) studied this question.