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Local existence and uniqueness for exterior static vacuum Einstein metrics


Author: Michael T. Anderson
Journal: Proc. Amer. Math. Soc. 143 (2015), 3091-3096
MSC (2010): Primary 83C20, 58D29, 58J32
Published electronically: February 5, 2015
MathSciNet review: 3336633
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Abstract: We study solutions to the static vacuum Einstein equations on domains of the form $ M \simeq \mathbb{R}^{3}\setminus B$ with prescribed Bartnik data $ (\gamma , H)$ on the inner boundary $ \partial M$. It is proved that for any smooth boundary data $ (\gamma , H)$ close to standard round data on the unit sphere $ (\gamma _{+1}, 2)$, there exists a unique asymptotically flat solution of the static vacuum Einstein equations realizing the boundary data $ (\gamma , H)$ which is close to the standard flat solution.


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Additional Information

Michael T. Anderson
Affiliation: Department of Mathematics, Stony Brook University, Stony Brook, New York 11794-3651
Email: anderson@math.sunysb.edu

DOI: https://doi.org/10.1090/S0002-9939-2015-12486-0
Received by editor(s): August 16, 2013
Received by editor(s) in revised form: February 14, 2014
Published electronically: February 5, 2015
Additional Notes: This work was partially supported by NSF grant DMS 1205947
Communicated by: Lei Ni
Article copyright: © Copyright 2015 American Mathematical Society