A scattering operator is an operator that characterises the behaviour of a field in terms of its asymptotic dynamics. In the context of conformal compactification, the asymptotic behaviour of the wave equation corresponds to its restriction to the conformal boundary (which represents the points at infinity in "physical spacetime"). The scattering operator then corresponds to trace operators that associate the initial data with its trace on the future and past boundaries. Here we are working in a dynamical spacetime: the Vaidya metric, which is a solution to Einstein's equation in the presence of null dust. During this talk I will present the conformal compactification of the Vaidya spacetime and explain how to construct the trace operators using vector field methods (also called energy estimates).
