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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.


The Theoretical Minimum Courses
Classical Mechanics (Fall 2007)
Classical Mechanics (Fall 2011)
Quantum Mechanics (Winter 2008)
Quantum Mechanics (Winter 2012)
Advanced Quantum Mechanics (Fall 2013)
Special Relativity (Spring 2008)
Special Relativity (Spring 2012)
Einstein's General Theory of Relativity (Fall 2008)
General Relativity (Fall 2012)
Cosmology (Winter 2009)
Cosmology (Winter 2013)
Statistical Mechanics (Spring 2009)
Statistical Mechanics (Spring 2013)
Particle Physics 1: Basic Concepts (Fall 2009)
Particle Physics 2: Standard Model (Spring 2010)
Particle Physics 3: Supersymmetry and Grand Unification (Spring 2010)
String Theory and M-Theory (Fall 2010)
Topics in String Theory (Cosmology and Black Holes) (Winter 2011)
Quantum Entanglements, Part 1 (Fall 2006)
Relativity (Spring 2007)