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<p>We prove a nonlinear characteristic <InlineEquation ID="IEq4"> <EquationSource Format="TEX">\(C^k\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mi>C</mi> <mi>k</mi> </msup> </math></EquationSource> </InlineEquation>-gluing theorem for vacuum gravitational fields in Bondi gauge for a class of characteristic hypersurfaces near static vacuum <i>n</i>-dimensional backgrounds, <InlineEquation ID="IEq5"> <EquationSource Format="TEX">\(n\ge 3\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>n</mi> <mo>≥</mo> <mn>3</mn> </mrow> </math></EquationSource> </InlineEquation>, with any finite <i>k</i>, with cosmological constant <InlineEquation ID="IEq6"> <EquationSource Format="TEX">\( \Lambda \in \mathbb {R}\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi mathvariant="normal">Λ</mi> <mo>∈</mo> <mi mathvariant="double-struck">R</mi> </mrow> </math></EquationSource> </InlineEquation>, near Birmingham-Kottler backgrounds. This generalises the <InlineEquation ID="IEq7"> <EquationSource Format="TEX">\(C^2\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mi>C</mi> <mn>2</mn> </msup> </math></EquationSource> </InlineEquation>-gluing of Aretakis, Czimek and Rodnianski, carried-out near light cones in four-dimensional Minkowski spacetime.</p>

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Characteristic Gluing with \(\Lambda \): III. High-Differentiability Nonlinear Gluing

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年1月12日

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  • Piotr T. Chruściel,
  • Wan Cong,
  • Finnian Gray

摘要

We prove a nonlinear characteristic \(C^k\) C k -gluing theorem for vacuum gravitational fields in Bondi gauge for a class of characteristic hypersurfaces near static vacuum n-dimensional backgrounds, \(n\ge 3\) n ≥ 3 , with any finite k, with cosmological constant \( \Lambda \in \mathbb {R}\) Λ ∈ R , near Birmingham-Kottler backgrounds. This generalises the \(C^2\) C 2 -gluing of Aretakis, Czimek and Rodnianski, carried-out near light cones in four-dimensional Minkowski spacetime.