Professor Susskind continues the discussion of black hole physics. He begins by reviewing the Schwarzschild metric, and how it results in the event horizon of a black hole. Light rays can orbit a black hole. Professor Susskind derives the equations of motion for such an orbit using classical mechanics and the conservation of energy and angular momentum. This derivation yields the photon sphere at the orbital radius of a light ray around a black hole. Professor Susskind then moves on to the physics of the event horizon of a black hole. An in-falling observer experiences nothing unusual at the event horizon, but to an outside observer, it takes an infinite amount of time for the in-falling observer to reach the horizon. The physics of the horizon are analyzed using the hyperbolic coordinates of a uniformly accelerated reference frame. One inside the horizon, in-falling objects cannot avoid the singularity at the center of a black hole because the radial dimension effectively becomes a time dimension and the singularity is a point in the future of every event. Topics: - Schwarzschild metric - Schwarzschild Radius - Black hole event horizon - Light ray orbiting a black hole - Photon sphere - Hyperbolic coordinates - Black hole singularity Recorded on October 29, 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.