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BIMSA General Relativity Seminar
BIMSA General Relativity Seminar
Solutions of the constraint equations with controlled decay to Kerr
Solutions of the constraint equations with controlled decay to Kerr
Organizers
Piotr Chrusciel
, Puskar Mondal
,
Bowen Zhao
Speaker
Andrea Nuetzi
Time
Tuesday, May 12, 2026 4:30 PM - 5:30 PM
Venue
A3-3-201
Online
Zoom 712 322 9571
(BIMSA)
Abstract
I will explain that to every small and decaying solution of the linearized constraint equations about Minkowski initial data, one can add a quadratically small correction to obtain a solution of the full constraint equations. Near spacelike infinity, the correction is given by Kerr black hole initial data, up to a term that decays faster than the linearized solution, and that has Schwartz decay if the linearized solution has Schwartz decay. The main tool is a right inverse (up to necessary integrability conditions) for the linearized constraint operator about Minkowski initial data, that has optimal mapping properties relative to weighted b-Sobolev spaces, where the weights measure decay towards infinity. Using a recent result, one obtains that the solutions of the Einstein equations with these initial data admit a regular conformal compactification along null and timelike infinity.