The celebrated Kerr family arise in General Relativity as spacetimes that contain a rotating black hole. Fundamental to their existence as physical objects is their (conjectured) stability as solutions to the vacuum Einstein equations. Under a certain poor man’s linearisation, one can relate this conjecture to the dispersion of waves on a fixed Kerr background, a statement which was only recently understood in a seminal paper of Dafermos,Rodnianski and Shlapentokh-Rothman. 

In this talk, we will discuss the simpler case of wave propagation on the Schwarzschild spacetime, which sits inside the Kerr family as a non-rotating black hole.