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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 04 - Volumes and Volume Elements; Conservation Laws

Volumes and volume elements, covariant construction using the Levi-Civita tensor. How to go between differential and integral formulations of conservation laws. Electrodynamics in geometric language (4-current, Faraday field tensor). Introduction of the stress-energy tensor, with the perfect fluid stress-energy tensor as a particularly important example.


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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
Lecture 12 - The Einstein Field Equation
Lecture 13 - The Einstein Field Equation (Variant Derivation)
Lecture 14 - Linearized Gravity I: Principles and Static Limit
Lecture 15 - Linearized Gravity II: Dynamic Sources
Lecture 16 - Gravitational Radiation I
Lecture 17 - Gravitational Radiation II
Lecture 18 - Cosmology I
Lecture 19 - Cosmology II
Lecture 20 - Spherical Compact Sources I
Lecture 21 - Spherical Compact Sources II
Lecture 22 - Black Holes I
Lecture 23 - Black Holes II