The conformal Einstein field equations and the local extension of future null infinity

TL;DR

This paper demonstrates that under specific initial data conditions, a portion of null infinity can be recovered, and it establishes the semi-global stability of Minkowski spacetime using conformal Einstein equations.

Contribution

It introduces an improved existence result for the characteristic initial value problem and applies it to prove semi-global stability of Minkowski spacetime.

Findings

Recovery of null infinity from initial data on null hypersurfaces

Establishment of semi-global stability of Minkowski spacetime

Extension of conformal Einstein equations theory

Abstract

We make use of an improved existence result for the characteristic initial value problem for the conformal Einstein equations to show that given initial data on two null hypersurfaces $\mathcal{N}_\star$ and $\mathcal{N}'_\star$ such that the conformal factor (but not its gradient) vanishes on a section of $\mathcal{N}_\star$ one recovers a portion of null infinity. This result combined with the theory of the hyperboloidal initial value problem for the conformal Einstein field equations allows to show the semi-global stability of the Minkowski spacetime from characteristic initial data.