A Perspicuous Description of the Schwarzschild Black Hole Geodesics

TL;DR

This paper provides a clear, analogue potential-based description of Schwarzschild black hole geodesics, analyzing light and particle trajectories with non-zero angular momentum, and compares GR predictions with Newtonian physics.

Contribution

It introduces an analogue potential approach to describe Schwarzschild geodesics, offering new insights into particle motion and the influence of angular momentum near black holes.

Findings

Relation between particle motion and angular momentum near the horizon

Comparison of GR and Newtonian physics using analogue potentials

Behavior of light and massive particles in Schwarzschild spacetime

Abstract

Schwarzschild black hole is the simplest black hole that is studied most in detail. Its behavior is best understood by looking at the geodesics of the particles under the influence of its gravitational field. In this paper, the focus of attention is giving a perspicuous description of the Schwarzschild geodesics by using analogue potential approach. Specifically we discuss geodesics of light and of a massive particle in the case that their angular momentum is non zero in the Schwarzschild spacetime. This discussion is done by defining analogue potentials out of geodesic equations and defining relevant dimensionless conserved quantities. Then, we designate how geodesics change in response to the change of these quantities. Our results indicate the relation between the particles' motion near black hole horizon and their angular momentum. Furthermore, we make a comparison between Newtonian Physics (NP) and General Relativity (GR) in the language of the analogue potential approach.