General Relativity is a major area of study in physics. It allows us to calculate the motion and interaction of particles in a non-Euclidean space-time. This presentation will examine the process of nding the Schwarzschild metric tensor eld by nding a solution of the Einstein Equation for a non-rotating spherical mass. A general form of the Schwarzschild metric tenor eld will be used to calculate the Riemann curvature tensor and subsequently the Ricci tensor and Ricci scalar which will be used to nd a vaccum solution to the Einstein Equation. Once the solutions of the Einstein Equation is found, they can be plugged into the Schwarzschild metric tensor eld and equations of motion can be calculated through the geodesic equation. This presentation will nd the orbits for massive particles moving around and into a black hole. Overall, this presentation will be an examination of the basic calculations that are done in General Relativity and it will show how matter moves in a curved space-time.
Ross, Matthew B., "The Schwarzschild Solution and Timelike Geodesics" (2015). Physics Capstone Project. Paper 29.