Lecture 6

In lecture 6, we completed our discussion of the Unruh effect. The central result that for a set of observers in region I, using Rindler modes, even the Minkowski vacuum appears to be a thermal density matrix. We then applied this intuition to black holes. There we found that locally, the change of coordinates from Schwarzschild coordinates to Kruskal coordinates was very similar to the transformation between Rindler and Minkowski coordinates. Correspondingly we guessed that the Bogoliubov coefficients between the Schwarzschild and the Kruskal modes should be the same as the Bogoliubov coefficients between the Rindler and the Minkowski modes. This led us to the remarkable conclusion that black holes appear to radiate particles like a black body with a temperature, T, that in the Schwarzschild case is just (1/(8 \pi M)).