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These notes contain a very simple review on QFT in curved spacetimes. Based on Winitzki, S. "Elementary Introduction to Quantum Fields in Curved Spacetime" and Wald, R. "Quantum Field Theory in Curved Spacetime and Black Hole Thermodynamics".
I thank V. Schomerus and F. Baume for the careful reading of these notes and A. Antunes for some interesting discussions on this topic. The part of the notes covered in the lecture starts at page 7.