Circular motion of test particles, trajectories and QPOs around the non-rotating black hole in the background of the Symmergent gravity

Abstract

We explore the circular motion of test particles around the non-rotating black hole in the background of the Symmergent gravity, focusing on how the parameters of the underlying model influence particle motion. The black hole is fully characterized by four parameters, namely, the mass $M$ of the black hole, the charge $q$ of the black hole, and two parameters $\eta$ and $\alpha$, with $\eta >1$ ($\eta <1$) corresponding to Ads (ds) spacetime. We derive the analytical solution of the energy and angular momentum of test particles as a function of parameters of the underlying model and discuss the stability of circular orbits through an effective potential approach. The innermost stable circular orbits and the effective force exerted on particles are examined. By numerical integration of the equations of motion, we plot the trajectories to investigate the motion of particles orbiting the black hole. Furthermore, we study the epicyclic oscillation of test particles that encircle the black hole near the equatorial plane and derive analytical equations for radial, orbital, and latitudinal frequencies as a function of the parameters of the model. The frequency of periastron precession of particles has also been discussed. Lastly, we consider the collision of particles near the event horizon and examine the center of mass-energy. Our findings reveal that the model parameters influence the motion of the test particles.