Einstein's General Theory of Relativity
Einstein's General Theory of Relativity (Fall 2008, Stanford Univ.). Instructor: Professor Leonard Susskind. General relativity, or the general theory of 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. (from theoreticalminimum.com)
| Lecture 01 - Newtonian Gravity and the equivalence principle Newtonian Gravity, Equivalence Principle, Gauss theorem. |
| Lecture 02 - Tidal forces and curvature Review preliminary mathematics, Tidal forces and curvature, Minkowski metric. |
| Lecture 03 - Essential tools: tensors and the metric Einstein summation convention, Distance element, Contravariant/covariant transformations, Metric tensor. |
| Lecture 04 - Tensor mechanics Tensors, Tensor indices, Inverse of the metric tensor, The metric tensor is symmetric, Proper time. |
| Lecture 05 - Covariant differentiation and geodesics Transformation properties of tensors, Covariant derivative, Christoffel symbol, Geodesic. |
| Lecture 06 - The flat space of special relativity The Minkowski metric, Minkowski space, Parallel transport. |
| Lecture 07 - The Riemannian curvature tensor Parallel Transport, Riemann curvature tensor, Ricci tensor, Continuity equation, Energy momentum tensor. |
| Lecture 08 - Equations of motion in curved space Covariant derivative, Riemann tensor, Newtonian approximation, Tangent vector, Curvature. |
| Lecture 09 - Gravitation in the Newtonian approximation The field equations of relativity in the Newtonian approximation, Einstein's equation relating curvature and the energy momentum tensor. |
| Lecture 10 - Energy-momentum tensor and Einstein's equations Wave equation for a scalar field in curved space, Energy momentum tensor, Cosmological constant. |
| Lecture 11 - Accelerated coordinates Local inertial coordinates, Rindler coordinates, Schwarzschild metric, Birkhoff's theorem. |
| Lecture 12 - World lines and Schwarzschild solution Space-time diagram, Light cone, Schwarzschild metric, Singularity, Event horizon. |
| References |
| General Relativity (Fall, 2008) | The Theoretical Minimum General relativity, or the general theory of relativity, is the geometric theory of gravitation published by Albert Einstein in 1916 and the current description of gravitation in modern physics. |