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On the Bartnik conjecture for the static vacuum Einstein equations
- Publication Year :
- 2015
-
Abstract
- We prove that given any smooth metric $\gamma$ and smooth positive function $H$ on $S^{2}$, there is a constant $\lambda > 0$, depending on $(\gamma, H)$, and an asymptotically flat solution $(M, g, u)$ of the static vacuum Einstein equations on $M = {\mathbb R}^{3} \setminus B^{3}$, such that the induced metric and mean curvature of $(M, g, u)$ at $\partial M$ are given by $(\gamma, \lambda H)$. This gives a partial resolution of a conjecture of Bartnik.<br />Comment: Substantial simplification of proof of main theorem. To appear in Class. Quantum Gravity
- Subjects :
- Mathematics - Differential Geometry
General Relativity and Quantum Cosmology
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.1507.05887
- Document Type :
- Working Paper
- Full Text :
- https://doi.org/10.1088/0264-9381/33/1/015001