8.962 General Relativity (Spring 2020, MIT OCW): Lecture 15 - Linearized Gravity II: Dynamic Sources

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 15 - Linearized Gravity II: Dynamic Sources

Solving the linearized field equation for a dynamical source. Using a radiative Green's function, we find an exact solution for this case. By carefully considering gauge and gauge-invariant spacetime components, we characterize the nature of the degrees of freedom encoded in this solution. Of particular relevance to the next two lectures is that two components of this solution describe gravitational radiation in a gauge-invariant manner. (It's worth reiterating that this lecture is somewhat advanced; students do not need to follow every detail in order to get the lecture's point.)

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