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

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 ${\mathcal{N}}_{\star }^{\prime }$ 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.

23 pages, 5 figures

References in corpus (3)

• On de Sitter-like and Minkowski-like space-times
• Revisiting the characteristic initial value problem for the vacuum Einstein field equations
• Global nonlinear stability of Minkowski space for spacelike-characteristic initial data

Cited by in corpus (1)

• Classical double copy at null infinity