Initial data for Minkowski stability with arbitrary decay

by Mr Arthur Touati (IHES)

Friday May 31, 2024, 1:30 PM → 3:30 PM Europe/Paris

1180 (Bât. E2) (Tours)

In this talk, I will present a construction of arbitrarily decaying initial data for the stability of Minkowski spacetime as solutions to the Einstein equations. Initial data on a spacelike hypersurface need to solve the so-called constraint equations, i.e a geometric nonlinear underdetermined elliptic system. I will show how one can parametrize solutions in a neighborhood of Minkowski spacetime and address linear obstructions coming from conservation laws in general relativity. This is a joint work with Allen Juntao Fang and Jérémie Szeftel.