A scattering theory construction of dynamical solitons

In the past 20 years the mathematical study of dynamical properties of black holes has greatly accelerated. Indeed, the first mathematical description of a dynamical black hole is from 2013. Many of the works focus on symmetry reduced settings, or toy problems that ought to capture important phenomenology of the Einstein equations. Outside a few exceptions, these works are focused on the solution in a neighbourhood of a single black hole, resulting in almost spherically symmetric setting in the far region. In this talk, I will present a model problem that I think captures some, albeit not all, important features and difficulties of studying multi black hole solutions in asymptotically flat spacetimes and report on progress in the understanding of this model. In particular, I will present the construction of a solution to the energy critical wave equation in a neighbourhood of timelike infinity that has a prescribed radiation field through null infinity.