#### Mentor

James T. Wheeler

#### Document Type

Report

#### Publication Date

1-28-2016

#### First Page

1

#### Last Page

13

#### Abstract

General Relativity is the standard theory of the gravitational interaction. It allows us to cal- culate the motions and interactions of particles in a non-Euclidean space-time. This presentation will present the derivation of the Schwarzschild metric tensor field by finding a solution of the Einstein Equation for a non-rotating, static vacuum. A general form of the metric for a static, spherically symmetric spacetime will be used to calculate the Riemann curvature tensor and sub- sequently the Ricci tensor and Ricci scalar which will then be used to find a vaccum solution to the Einstein Equation. Once the solutions of the Einstein equation are found, we can study the geodesic equation. This lets us find the orbits for massive particles moving around and into a black hole. Overall, this presentation provide an examination of the basic calculations that are done in General Relativity and shows how matter moves in a curved space-time.

#### Recommended Citation

Ross, Matthew, "The Schwarzschild Solution and Timelike Geodesics" (2016). *Physics Capstone Projects.* Paper 31.

https://digitalcommons.usu.edu/phys_capstoneproject/31