Trajectory around a spherically symmetric non-rotating black hole

TL;DR

This paper analyzes the trajectories of particles and light around spherical black holes, introduces a pseudo-Newtonian potential, and compares it with the effective potential, exemplified by the Reissner-Nordström black hole.

Contribution

It presents a new pseudo-Newtonian potential for spherical black holes and compares it with the effective potential, including specific results for Reissner-Nordström black holes.

Findings

Derived a pseudo-Newtonian potential for spherical black holes

Compared the potential with the effective potential for test particles

Presented example results for Reissner-Nordström black holes

Abstract

Trajectory of a test particle or a photon around a general spherical black hole is studied and bending of light trajectory is investigated. Pseudo-Newtonian gravitational potential describing the gravitational field of the black hole is determined and is compared with the related effective potential for test particle motion. As an example, results are presented for Reissner-Nordstr\"{o}m black hole.