Characteristic Gluing with $\mathrm{\Lambda }$: II. Linearised equations in higher dimensions

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 $\mathrm{\Lambda }\in \mathbb{R}$, $n\ge 4$. This generalises, in the linearised case, the pioneering analysis of Aretakis, Czimek and Rodnianski, carried-out on light cones in four-dimensional Minkowski spacetime.