Existence of static vacuum extensions with prescribed Bartnik boundary data

2021/03/29 by Zhongshan An, An, Zhongshan, Lan-Hsuan Huang +1 · 2 citations
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #Geometric Analysis and Curvature Flows #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.2103.15887

openalex publication_date 2021/03/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove the existence and local uniqueness of asymptotically flat, static vacuum metrics with arbitrarily prescribed Bartnik boundary data that are close to the induced boundary data on any star-shaped hypersurface or a general family of perturbed hypersurfaces in the Euclidean space. It confirms the existence part of the Bartnik static extension conjecture for large classes of boundary data, and the static vacuum metric obtained is geometrically unique in a neighborhood of the Euclidean metric.

Cited by

• Cohomology for linearized Ricci curvature
• Local Well-Posedness for the Bartnik Stationary Extension Problem near Schwarzschild Spheres

Related

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• Ellipticity of Bartnik boundary data for stationary vacuum spacetimes
• Static vacuum Einstein metrics on bounded domains
• Uniqueness of static vacuum Einstein metrics and the Bartnik quasi-local mass
• Local Well-Posedness for the Bartnik Stationary Extension Problem near Schwarzschild Spheres