General Relativity

This course introduces the foundations of general relativity - Einstein's theory of gravitational interactions - with applications. We begin with a physical motivation for general relativity in terms of the equivalence principle and tidal forces. We then develop the mathematical framework of differential geometry needed for working in curved space-time. Equipped with the machinery of connections, covariant derivatives, and the Riemann curvature tensor we will investigate the geodesic equations and Einstein's equations, which describe the dynamic relationship between matter and geometry. Applications will include the determination of orbits near stars and black holes, and the bending of light.