Please note the special day, time and location.  The study of graviton Hawking radiation, renormalized interactions of dynamical gravitons with other matter fields, and quantum back reaction of Hawking radiation on the black hole horizon all require the knowledge of the graviton propagator on a black hole spacetime. I will discuss an explicit mode-decomposed construction of the de Donder gauge graviton propagator for the Unruh state on the eternal Schwarzschild spacetime.  De Donder gauge is chosen for its covariance and locality properties. This is joint work with F. Bussola (Pavia).