Abstract We prove a nonlinear characteristic Cᵏ C k -gluing theorem for vacuum gravitational fields in Bondi gauge for a class of characteristic hypersurfaces near static vacuum n -dimensional backgrounds, n 3 n ≥ 3, with any finite k, with cosmological constant R Λ ∈ R, near Birmingham-Kottler backgrounds. This generalises the C² C 2 -gluing of Aretakis, Czimek and Rodnianski, carried-out near light cones in four-dimensional Minkowski spacetime.
Chruściel et al. (Mon,) studied this question.