General Relativity and Penrose process

Abstract Using the concept of parallel transport of vectors in curved manifolds, the Riemann curvature tensor in terms of Christoffel symbols is obtained. Making use of the Riemann curvature tensor’s symmetry properties, the Ricci curvature tensor and Einstein’s tensor are derived. Through Einstein’s tensor and the Poisson equation for Newtonian gravity, the Einstein field equations are introduced. Upon using Kerr metric (Kerr, 1963) as a solution for Einstein’s field equations, extraction of energy from a rotating black hole is proved. This is called the Penrose process (Penrose and Floyd, 1971).