### 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 B̄
_{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 = ℝ
^{3}\B
_{1} such that it satisfies Bartnik's geometric boundary condition on ∂ B
_{1}.

Original language | English (US) |
---|---|

Pages (from-to) | 27-46 |

Number of pages | 20 |

Journal | Communications in Mathematical Physics |

Volume | 241 |

Issue number | 1 |

State | Published - Oct 2003 |

Externally published | Yes |

### Fingerprint

### ASJC Scopus subject areas

- Mathematical Physics
- Physics and Astronomy(all)
- Statistical and Nonlinear Physics

### Cite this

*Communications in Mathematical Physics*,

*241*(1), 27-46.

**On Existence of Static Metric Extensions in General Relativity.** / Miao, Pengzi.

Research output: Contribution to journal › Article

*Communications in Mathematical Physics*, vol. 241, no. 1, pp. 27-46.

}

TY - JOUR

T1 - On Existence of Static Metric Extensions in General Relativity

AU - Miao, Pengzi

PY - 2003/10

Y1 - 2003/10

N2 - 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 B̄ 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 = ℝ 3\B 1 such that it satisfies Bartnik's geometric boundary condition on ∂ B 1.

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 B̄ 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 = ℝ 3\B 1 such that it satisfies Bartnik's geometric boundary condition on ∂ B 1.

UR - http://www.scopus.com/inward/record.url?scp=0142199386&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0142199386&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0142199386

VL - 241

SP - 27

EP - 46

JO - Communications in Mathematical Physics

JF - Communications in Mathematical Physics

SN - 0010-3616

IS - 1

ER -