Lecture 8: More on the Schwarzschild black hole and dust collapse
In this lecture, we completed our discussion of the Schwarzschild black hole by reviewing its Penrose diagram. This solution is particularly important because it is the unique vacuum solution with spherical symmetry; this fact is known as Birkhoff's theorem. Schwarzschild black holes can also be found in higher dimensions, and we quickly reviewed these solutions.
We then turned to black holes formed by collapse. Using techniques developed by B. Datt, Oppenheimer and Snyder were able to follow the collapse of dust into a singularity. The key trick is to go to a co-moving frame for the dust, where the stress-tensor simplifies considerably. We also reviewed radial geodesics in this geometry; the horizon is a light ray that gets trapped by the collapse. Light rays that come in a little earlier can escape after spending some time near the horizon; light rays that come in later are trapped and collapse onto the singularity.
A translation of Datt's paper is available here. [this is behind a paywall, so you will need to be at an institute IP to access this.]
The Oppenheimer-Snyder paper is available here. [This is freely available; not behind a paywall.]
