Abstract

I will talk about the scattering problem in general relativity, and present a construction of a scattering theory for the linearised Einstein equations in a double null gauge against a Schwarzschild background. The construction begins by dealing with the gauge invariant components of the linearised system via the spin $\pm2$ Teukolsky equations and the Teukolsky—Starobinsky identities; this was the subject of the paper arXiv:2007.13658. In this talk I will discuss how this theory can then be extended to the full system. Key to this step is the identification of suitable asymptotic gauge conditions on scattering data. Here, a Bondi-adapted double null gauge is shown to provide the necessary gauge rigidity, in a manner that enables the identification of Hilbert-space isomorphism between finite energy scattering data and a suitable space of finite energy Cauchy data. In particular, the scattering theory we construct enables us to show that, in the global scattering problem, the linear memory effects at past and future null infinity are related by an antipodal map on the 2-sphere.