Description: An examination of local coordinate transformations: proof that the metric of spacetime can be put into a representation that is locally flat (with “leftover” degrees of freedom corresponding to boosts and rotation). Deviations from flatness correspond to spacetime curvature. This lecture also discusses the notion of transport, which must be used to connect points in a manifold in order to define a proper tensor derivative. Focus here is on “parallel transport,” which turns out to use the Christoffel symbol introduced in Lecture 5.

Instructor: Prof. Scott Hughes