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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.


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)