8.962 General Relativity (Spring 2020, MIT OCW): Lecture 07 - The Principle of Equivalence (cont.); Parallel Transport

8.962 General Relativity

8.962 General Relativity (Spring 2020, MIT OCW). Instructor: Prof. Scott Hughes. 8.962 is MIT's graduate course in general relativity, which covers the basic principles of Einstein's general theory of relativity, differential geometry, experimental tests of general relativity, black holes, and cosmology. (from ocw.mit.edu)

Lecture 07 - The Principle of Equivalence (cont.); Parallel Transport

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.

Go to the Course Home or watch other lectures:

Lecture 01 - Introduction and the Geometric Viewpoint on Physics

Lecture 02 - Introduction to Tensors

Lecture 03 - Tensors (cont.)

Lecture 04 - Volumes and Volume Elements; Conservation Laws

Lecture 05 - The Stress Energy Tensor and the Christoffel Symbol

Lecture 06 - The Principle of Equivalence

Lecture 07 - The Principle of Equivalence (cont.); Parallel Transport

Lecture 08 - Lie Transport, Killing Vectors, Tensor Densities

Lecture 09 - Geodesics

Lecture 10 - Spacetime Curvature

Lecture 11 - More on Spacetime Curvature