This theorem demonstrates nonlinear gluing for vacuum gravitational fields in characteristic hypersurfaces, suggesting implications for higher-dimensional spacetimes.
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 Λ ∈ 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.
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Chruściel et al. (2026) studied this question.
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