General Relativity
General Relativity (Fall 2012, Stanford Univ.). Instructor: Professor Leonard Susskind. General relativity is the geometric theory of gravitation published by Albert Einstein in 1916 and the current description of gravitation in modern physics. General relativity generalises special relativity and Newton's law of universal gravitation, providing a unified description of gravity as a geometric property of space and time, or spacetime. In particular, the curvature of spacetime is directly related to the energy and momentum of whatever matter and radiation are present. This course uses the physics of black holes extensively to develop and illustrate the concepts of general relativity and curved spacetime. (from theoreticalminimum.com)
| Lecture 01 - The equivalence principle and tensor analysis A broad introduction to general relativity, The equivalence principle, Accelerated reference frames, Curvilinear coordinate transformations, Tensor analysis. |
| Lecture 02 - Tensor mathematics Review the geometries of flat and curved spaces, Metric tensor, Tensor analysis, Tensor mathematics: addition, multiplication, contraction. |
| Lecture 03 - Flatness and curvature Riemannian geometry, Metric tensor, Gaussian normal coordinates, Covariant derivatives, Christoffel symbols, Curvature tensor. |
| Lecture 04 - Geodesics and gravity Parallel transport, Tangent vectors, Geodesics, Spacetime, Special relativity, Uniform acceleration, Uniform gravitational fields. |
| Lecture 05 - Metric for a gravitational field The metric for a gravitational field, Space-like, time-like, and light-like intervals, Light cone, Black holes, Schwarzschild metric, Event horizon. |
| Lecture 06 - Black holes Schwarzschild metric, Schwarzschild Radius, Black hole event horizon, Light ray orbiting a black hole, Photon sphere, Hyperbolic coordinates, Black hole singularity. |
| Lecture 07 - Falling in to a black hole The in-depth discussion of the physics of black holes, Schwarzschild metric, Event horizon, Singularity. |
| Lecture 08 - Formation of a black hole Kruskal-Szekeres coordinates, Penrose diagrams, Wormholes, Formation of a black hole, Newton's shell theorem. |
| Lecture 09 - Einstein field equations Newtonian gravitational field, Continuity equation, The energy-momentum tensor, Curvature scalar, Ricci tensor, Einstein tensor, Einstein field equations. |
| Lecture 10 - Gravity waves Weak gravitational fields, Gravitational radiation, Gravity waves, Einstein-Hilbert action for general relativity. |
| References |
| General Relativity (Fall, 2012) | The Theoretical Minimum General relativity is the geometric theory of gravitation published by Albert Einstein in 1916 and the current description of gravitation in modern physics. |