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In our prior work toward Bartnik’s static vacuum extension conjecture for near Euclidean boundary data, we establish a sufficient condition, called static regular, and confirm that large classes of boundary hypersurfaces are static regular. In this paper, we further improve some of those prior results. Specifically, we show that any hypersurface in an open and dense subfamily of a certain general smooth one-sided family of hypersurfaces (not necessarily a foliation) is static regular. The proof uses some of our new arguments motivated from studying the conjecture for boundary data near an arbitrary static vacuum metric.
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Static Vacuum Extensions With Prescribed Bartnik Boundary Data Near a General Static Vacuum Metric
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.
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- Award ID(s):
- 2005588
- PAR ID:
- 10552861
- Publisher / Repository:
- Springer
- Date Published:
- Journal Name:
- Annals of PDE
- Volume:
- 10
- Issue:
- 1
- ISSN:
- 2524-5317
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1007/s40818-024-00169-w
