In our last lecture on QFT in curved spacetime, we completed our analysis from Lecture 5. We showed that unless the Rindler occupation numbers had the right thermal form, we would not be able to derive the short-distance behaviour of correlators in the Minkowski vacuum.
This derivation is important since it just relies on local properties of correlation functions, and generalizes easily to the late-time collapsing black hole geometry and other situations, where a global analysis of the modes may be difficult.
We also discussed Unruh detectors.