In this talk, I will describe recent and upcoming work on the asymptotic behaviour of gravitational radiation (linearised gravity around Schwarzschild) in a neighbourhood of spacelike infinity including past and future null infinity.
I will first set up a mathematical scattering framework in which one can understand the question of smoothness of null infinity on physical grounds.
I will then use this framework to present a basic sketch of the proof of the irregularity of null infinity in various physically motivated settings, together with a complete description of the semiglobal asymptotics of gravitational radiation one obtains instead.
In particular, I will discuss how a class of asymptotic conservation laws related to the Newman-Penrose charges can be used to infer the asymptotics for fixed angular modes, and describe how to use a persistence of polyhomogeneity result to sum up the individual angular modes.
Based on joint work with Hamed Masaood and Istvan Kadar.