**Copyright Information:**All rights reserved to Prof. Leonard Susskind, Stanford University.

### Lecture Description

Prof. Susskind develops the coordinate transformations used to create Penrose diagrams, and then uses them to describe the physics of black hole creation. He begins the lecture with a review of Kruskal coordinates, and how they apply to the study of black holes. He then moves on to develop a coordinate system which allows the depiction of all of spacetime on a finite blackboard. This results in a Penrose diagram for flat spacetime. The Penrose diagram for black holes leads to an understanding of wormholes, also known as Einstein-Rosen bridges. Professor Susskind then describes the process of black hole formation through the simplest possible mechanism: an infalling sphere of radiation. This process is studied by marrying a Penrose diagram for the flat spacetime inside the sphere, with a Penrose diagram for the black hole under formation outside the sphere of radiation. The boundary between the two diagrams is the radiation sphere itself, and this approach demonstrates how the black hole horizon develops and begins to expand even before the black hole itself forms. Topics: - Kruskal–Szekeres coordinates - Penrose diagrams - Wormholes - Formation of a black hole - Newton's shell theorem Recorded on November 12, 2012.

### Course Index

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

### Course Description

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.