Characteristic Gluing with Λ: III. High-differentiability nonlinear gluing

2024/07/04 by Chruściel, Piotr T., Cong, Wan, Gray, Finnian
#Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #Mathematical Physics (math-ph)

paper · doi:10.48550/arxiv.2407.03903

Abstract

We prove a nonlinear characteristic 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, with any finite k, with cosmological constant Λ∈ ℝ, near Birmingham-Kottler backgrounds. This generalises the C²-gluing of Aretakis, Czimek and Rodnianski, carried-out near light cones in four-dimensional Minkowski spacetime.

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