8.962 General Relativity (Spring 2020, MIT OCW): Lecture 08 - Lie Transport, Killing Vectors, Tensor Densities

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 08 - Lie Transport, Killing Vectors, Tensor Densities

Discussion of a second notion of transport, "Lie" transport, and the associated Lie derivative. Use of this derivative to discuss spacetime symmetries, as encapsulated by Killing vectors. Also discusses "tensor densities," volume elements in general spacetimes, and certain tricks and identities that use the determinant of the spacetime metric.

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