Recovering 5D geometry from amplitudes

It is well-known that physicists are amazing at computing two seemingly different things: geometries satisfying some gravitational equations of motion and scattering amplitudes. As physical objects, amplitudes encode quantum behaviour. However, over the last decade, significant effort has gone into understanding their classical limits and associated observables. While having a dictionary between amplitudes and classical physics is a great achievement, what keeps (some of) us going is the hope and excitement of exploring the dynamics of complex gravitational phenomena such as black hole mergers and the response of astrophysical objects to passing gravitational waves. One first step in this direction is to study the linear versions of these problems, while an even more modest step is to study the linearized backgrounds themselves. In this talk, I will introduce massive higher-spin amplitudes in four dimensions, talk about the way they model black hole scattering and how to massage them to extract classical data. I will then ask the same questions in five dimensions, where gravitational phenomena are richer and provide some clues to the amplitudes' take on these conundrums.