The Behaviour of Test Particles in the Vicinity of a Stationary Black Hole

Abstract: Studying general relativity, with spacetime as a curved four-dimensional pseudo-Riemannian space, much of ones physical intuition is lost. Furthermore, there no longer exists any canonical way to visualise this space, in which all other physics take place. In this paper, different representations of the Schwarzschild solution are studied, in an attempt to build up an intuitive understanding of the behaviour of test particles in the vicinity of a spherically symmetric and stationary source of gravity, such as a black hole. Three representations of the Schwarzschild solution will be studied; the original Schwarzschild representation, as well as the Fronsdal embedding and Kruskal-Szekeres transform.