Characteristic gluing with $\Lambda$: 1. Linearised Einstein equations on four-dimensional spacetimes

We establish a gluing theorem for linearised vacuum gravitational fields in Bondi gauge on a class of characteristic hypersurfaces in static vacuum four-dimensional backgrounds with cosmological constant $\Lambda \in \mathbb{R}$ and arbitrary topology of the compact cross-sections of the null hypersurface. This generalises and complements, in the linearised case, the pioneering analysis of Aretakis, Czimek and Rodnianski, carried-out on light-cones in Minkowski spacetime.

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Received 20 April 2023

Accepted 22 January 2024

Published 17 July 2024