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

19 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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10.1007/s00220-003-0925-2

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title = "On Existence of Static Metric Extensions in General Relativity",

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.",

author = "Pengzi Miao",

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AB - 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.

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On Existence of Static Metric Extensions in General Relativity

Abstract

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