Imprints of quantum gravity on periastron precession and trajectories around a black hole

Abstract

We investigate the motion of test particles around a spherically symmetric, non-rotating black hole within the framework of quantum gravity, emphasizing the impact of model parameters on particle dynamics. The black hole is characterized by its mass $M$ and two dimensionless parameters, $\alpha$ and $\beta$. Using the effective potential method, we analyze the stability of circular orbits and derive analytical expressions for the energy and angular momentum of test particles as functions of the black hole parameters. Additionally, we examine effective forces, determine the innermost stable circular orbits, and numerically integrate the equations of motion to study diverse particle trajectories. Analytical formulas for radial, vertical, and orbital frequencies, as well as the periastron precession frequency, are found from the exploration of epicyclic oscillations close to the equatorial plane. Lastly, we determine the center-of-mass energy for particle collisions close to the black hole horizon. Our results provide insights into the interaction between quantum gravity effects and black hole dynamics, explaining the substantial influence of $\alpha$ and $\beta$ on particle motion.