Geodesic Motions near an improved Schwarzschild black hole

TL;DR

This paper investigates the geodesic motions of particles near an improved Schwarzschild black hole, analyzing stability, horizons, and orbital dynamics using both equations of motion and dynamical systems methods.

Contribution

It provides a detailed analysis of particle trajectories, stability, and horizons in an improved Schwarzschild black hole, including the innermost stable circular orbit and phase space stability.

Findings

Only one horizon exists for the improved Schwarzschild black hole.

The innermost stable circular orbit radius has been determined.

Dynamical systems approach reveals stability and fixed points of geodesic trajectories.

Abstract

In this paper, we studied the geodesics of timelike and null like particles near an improved Schwarzschild black hole. The lapse function has been plotted and was found that only one horizon is possible. The equation of motion and effective potential of test particle have been calculated. This equation has an importance in studying the radial free fall and in studying the stability of radial orbits (trajectories). The energy and angular momentum have also been calculated to analysis the cicrular motion and stability of circular orbits. Moreover, Innermost stable circular orbit radius has determined. To get a deeper insight of the nature of these trajectories, we have studied the timelike and null geodesics with the help of the dynamical systems approach. This analysis help us to determine the stability as well as fixed point of phase space trajectories.