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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Local existence and uniqueness for exterior static vacuum Einstein metrics
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by Michael T. Anderson PDF
Proc. Amer. Math. Soc. 143 (2015), 3091-3096 Request permission

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
  • 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
  • © Copyright 2015 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 143 (2015), 3091-3096
  • MSC (2010): Primary 83C20, 58D29, 58J32
  • DOI: https://doi.org/10.1090/S0002-9939-2015-12486-0
  • MathSciNet review: 3336633