General Relativity

Fall, 2012

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. (Source: Wikipedia)

This course uses the physics of black holes extensively to develop and illustrate the concepts of general relativity and curved spacetime.

(Image credit: Ute Kraus, Max-Planck-Institut für Gravitationsphysik, Golm, and Theoretische Astrophysik, Universität Tübingen)

Lectures in this Course

  1. 1

    The equivalence principle and tensor analysis

    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'... [more]
  2. 2

    Tensor mathematics

    This lecture focuses on the mathematics of tensors, which represent the core concepts of general relativity. Professor Susskind opens the lecture with a brief review the geometries of flat and curved spaces. He then develops the mathematics of... [more]
  3. 3

    Flatness and curvature

    In this lecture, Professor Susskind presents the mathematics required to determine whether a spatial geometry is flat or curved. The method presented is to find a diagnostic quantity which, if zero everywhere, indicates that the space is flat. This... [more]
  4. 4

    Geodesics and gravity

    Professor Susskind begins the lecture with a review of covariant and contravariant vectors and derivatives, and the method for determining whether a space is flat. He then introduces the concept of geodesics, which are the straightest paths between... [more]
  5. 5

    Metric for a gravitational field

    In this lecture, Professor Susskind derives the metric for a gravitational field, and introduces the relativistic mathematics that describe a black hole. He begins by reviewing the concept of light cones and space- and time-like intervals from... [more]
  6. 6

    Black holes

    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... [more]
  7. 7

    Falling in to a black hole

    Professor Susskind continues the in-depth discussion of the physics of black holes. He begins with the Schwarzschild metric and then applies coordinate transformations to demonstrate that spacetime is nearly flat in the vicinity of the event... [more]
  8. 8

    Formation of a black hole

    Professor Susskind 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... [more]
  9. 9

    Einstein field equations

    Professor Susskind derives the Einstein field equations of general relativity.  Beginning with Newtonian gravitational fields, an analogy with the four-current, and the continuity equation, he develops the stress-energy tensor (also known as the... [more]
  10. 10

    Gravity waves

    Professor Susskind demonstrates how Einsteins's equations can be linearized in the approximation of a weak gravitational field. The linearized equation is a wave equation, and the solution to these equations create the theory of gravitational... [more]