The principle of equivalence of gravity and acceleration, or gravitational and inertial mass is the fundamental basis of general relativity. This was Einstein's key insight. Professor Susskind begins the first lecture of the course with Einstein's derivation of this equivalence principle. He then moves on to the mathematics of general relativity, including generalized coordinate transformations and tensor analysis. This topic includes the important point that the determination as to whether a spatial geometry is flat (i.e. Euclidean) is equivalent in some respects to the determination of whether an object is in a gravitational field, or merely an accelerated reference frame. Topics: - The equivalence principle - Accelerated reference frames - Curvilinear coordinate transformations - Effect of gravity on light - Tidal forces - Euclidean geometry - Riemannian geometry - Metric tensor - Distance measurement in a curved geometry - Intrinsic geometry - Flat spacetime - Einstein summation convention - Covariant and contravariant vectors and tensors Recorded on September 24, 2012.

1. The Equivalence Principle and Tensor Analysis
2. Tensor Mathematics
3. Riemannian Geometry: Flatness and Curvature
4. Geodesics, Gravitational Fields, & Special Relativity
5. The Metric for a Gravitational Field
6. Schwarzschild Radius & Black Hole Singularity
7. Falling into a Black Hole: The Event Horizon
8. Black Hole Formation, Penrose Diagrams & Wormholes
9. Einstein Field Equations of General Relativity
10. Gravity Waves: Gravitational Radiation & Einstein-Hilbert Action

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 generalizes 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. This series is the fourth installment of a six-quarter series that explore the foundations of modern physics. In this quarter, Leonard Susskind focuses on Einstein's General Theory of Relativity.