Local existence and uniqueness for exterior static vacuum Einstein metrics

Anderson, Michael

doi:10.1090/S0002-9939-2015-12486-0

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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