Effects of Two Quantum Correction Parameters on Chaotic Dynamics of Particles Near Renormalized Group Improved Schwarzschild Black Holes

TL;DR

This study investigates how two quantum correction parameters influence the chaotic behavior of particles near a renormalized Schwarzschild black hole, revealing that one parameter significantly enhances chaos while the other has minimal effect.

Contribution

It provides a detailed analysis of the distinct roles of two quantum correction parameters on particle chaos, constrained by observational data from M87*.

Findings

Small changes in $\gamma$ have negligible effect on chaos.

Decreasing $\Omega$ enhances the strength of chaos.

The parameter $\Omega$ acts as a dominant factor in chaos dynamics.

Abstract

A renormalized group improved Schwarzschild black hole spacetime contains two quantum correction parameters. One parameter $\gamma$ represents the identification of cutoff of the distance scale, and another parameter $\Omega$ stems from nonperturbative renormalization group theory. The two parameters are constrained by the data from the shadow of M87* central black hole. The dynamics of electrically charged test particles around the black hole are integrable. However, when the black hole is immersed in an external asymptotically uniform magnetic field, the dynamics are not integrable and may allow for the occurrence of chaos. % English Editor: %Please verify that the intended meaning has been retained. Employing an explicit symplectic integrator, we survey the contributions of the two parameters to the chaotic dynamical behavior. It is found that a small change of the parameter $\gamma$ constrained by the shadow of M87* black hole has an almost negligible effect on the dynamical transition of particles from order to chaos. However, a small decrease in the parameter $\Omega$ leads to an enhancement in the strength of chaos from the global phase space structure. A theoretical interpretation is given to the different contributions. The term with the parameter $\Omega$ dominates the term with the parameter $\gamma$, even if the two parameters have same values. % English Editor: Please verify %that the intended meaning has been retained. In particular, the parameter $\Omega$ acts as a repulsive force, and its decrease means a weakening of the repulsive force or equivalently enhancing the attractive force from the black hole. On the other hand, there is a positive Lyapunov exponent that is universally given by the surface gravity of the black hole when $\Omega\geq 0$ is small and the external magnetic field vanishes.