A Perspicuous Description of the Schwarzschild Black Hole Geodesics

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.
Comment: 6 pages, 3 figures