Characteristic gluing to the Kerr family and application to spacelike gluing

TL;DR

This paper develops a characteristic gluing method for Einstein vacuum equations, enabling the connection of asymptotically flat data to Kerr spacetimes and providing an alternative proof for spacelike gluing.

Contribution

It introduces a detailed characteristic gluing technique including 10 charges, relating them to physical quantities and applying this to spacelike gluing constructions.

Findings

Successfully glues asymptotically flat data to Kerr spacetime.

Provides an alternative proof of the Corvino-Schoen spacelike gluing.

Relates charges to ADM energy, momentum, and angular momentum.

Abstract

This is the third paper in a series of papers adressing the characteristic gluing problem for the Einstein vacuum equations. We provide full details of our characteristic gluing (including the $10$ charges) of strongly asymptotically flat data to the data of a suitably chosen Kerr spacetime. The choice of the Kerr spacetime crucially relies on relating the $10$ charges to the ADM energy, linear momentum, angular momentum and the center-of-mass. As a corollary, we obtain an alternative proof of the Corvino-Schoen spacelike gluing construction for strongly asymptotically flat spacelike initial data.