Null asymptotics of perturbations of Minkowski spacetime

Seminar in Mathematics

Abstract: In the context of perturbations of Minkowski spacetime in general relativity, there are interesting open questions about asymptotics and scattering: Under what conditions do perturbations admit a smooth conformal compactification at null infinity? How is the radiative null asymptotics rigorously described by the physical scattering amplitudes? I will explain results motivated by these questions and outline how they may be answered. First, the construction of a b-pseudodifferential chain homotopy for the de Rham complex, that can be used to solve the constraint PDE with precise control over asymptotics. Second, I will indicate how one can formulate the dynamic problem as a quasilinear, symmetric hyperbolic PDE that is regular at null infinity, and with null infinity being at a fixed locus. It is not regular at spacelike infinity due to the asymptotics of the Kerr spacetime, which requires tailored energy estimates.