Black holes

General Relativity (Fall, 2012)

October 29, 2012

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.

  • Schwarzschild metric
  • Schwarzschild Radius
  • Black hole event horizon
  • Light ray orbiting a black hole
  • Photon sphere
  • Hyperbolic coordinates
  • Black hole singularity