Static vacuum extensions with prescribed Bartnik boundary data near a general static vacuum metric

Abstract

We introduce the notions of static regular of type (I) and type (II) and show that they are sufficient conditions for local well-posedness of solving asymptotically flat, static vacuum metrics with prescribed Bartnik boundary data. We then show that hypersurfaces in a very general open and dense family of hypersurfaces are static regular of type (II). As applications, we confirm Bartnik's static vacuum extension conjecture for a large class of Bartnik boundary data, including those that can be far from Euclidean and have large ADM masses, and give many new examples of static vacuum metrics with intriguing geometry.

arXiv commentv2 matches the version that appeared in the Annals of PDE. Comments welcome!

References in corpus (6)

• On boundary value problems for Einstein metrics
• On the Bartnik extension problem for the static vacuum Einstein equations
• On Existence of Static Metric Extensions in General Relativity
• Embeddings, immersions and the Bartnik quasi-local mass conjectures
• New asymptotically flat static vacuum metrics with near Euclidean boundary data
• A flow approach to Bartnik's static metric extension conjecture in axisymmetry