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On Existence of Static Metric Extensions in General Relativity

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Abstract

Motivated by problems related to quasi-local mass in general relativity, we study the static metric extension conjecture proposed by R. Bartnik [4]. We show that, for any metric on ¯B 1 that is close enough to the Euclidean metric and has reflection invariant boundary data, there always exists an asymptotically flat and scalar flat static metric extension in M=ℝ3∖B 1 such that it satisfies Bartnik's geometric boundary condition [4] on ∂B 1.

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Authors and Affiliations

  1. Department of Mathematics, Stanford University, CA, 94305, USA

    Pengzi Miao

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  1. Pengzi Miao
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Correspondence to Pengzi Miao.

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Communicated by G.W. Gibbons

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Miao, P. On Existence of Static Metric Extensions in General Relativity. Commun. Math. Phys. 241, 27–46 (2003). https://doi.org/10.1007/s00220-003-0925-2

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  • DOI: https://doi.org/10.1007/s00220-003-0925-2

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