Long time existence from interior gluing

TL;DR

This paper proves the existence of a region near spatial infinity in asymptotically flat spacetimes using a gluing method and stability theorem, despite potential issues with metric smoothness.

Contribution

It introduces a novel gluing construction combined with scaling techniques to establish existence results near spatial infinity for general asymptotically flat data.

Findings

Existence of a piece of Scri near $i^0$ for general data

Reduction of the problem to Bieri's stability theorem

Handling of potential poor differentiability of the conformally rescaled metric

Abstract

We prove the "existence of a piece of Scri near $i^0$" (with most likely poor differentiability of the conformally rescaled metric) for general asymptotically flat data with well-defined energy-momentum. The proof uses scaling and a gluing construction to reduce the problem to Bieri's stability theorem.