Characteristic Gluing with $\hat{I}›$: II. Linearised equations in higher dimensions

Abstract

We prove a gluing theorem for linearised vacuum gravitational fields in Bondi gauge on a class of characteristic hypersurfaces in static vacuum $(n+1)$-dimensional backgrounds with cosmological constant $\hat{I}›\in \mathbb{R}$, $n\ge 4$. This generalises, in the linearised case, the pioneering analysis of Aretakis, Czimek and Rodnianski, carried-out on light cones in four-dimensional Minkowski spacetime.

v2; update includes changes and additions to streamline compatibility with part III---the nonlinear gluing. 145 pages, 72 main text plus appendices and index, 4 figures, results summarised in 4 tables