On Existence of Static Metric Extensions in General Relativity

Pengzi Miao

doi:10.1007/s00220-003-0925-2

On Existence of Static Metric Extensions in General Relativity

Pengzi Miao

Research output: Contribution to journal › Article › peer-review

21 Scopus citations

Abstract

Motivated by problems related to quasi-local mass in general relativity, we study the static metric extension conjecture proposed by R. Bartnik. We show that, for any metric on B̄₁ 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\B₁ such that it satisfies Bartnik's geometric boundary condition on ∂ B₁.

Original language	English (US)
Pages (from-to)	27-46
Number of pages	20
Journal	Communications in Mathematical Physics
Volume	241
Issue number	1
DOIs	https://doi.org/10.1007/s00220-003-0925-2
State	Published - Oct 2003
Externally published	Yes

ASJC Scopus subject areas

Statistical and Nonlinear Physics
Mathematical Physics

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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. 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\B1 such that it satisfies Bartnik's geometric boundary condition on ∂ B1.",

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