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 |
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ASJC Scopus subject areas
- Mathematical Physics
- Physics and Astronomy(all)
- Statistical and Nonlinear Physics
Cite this
On Existence of Static Metric Extensions in General Relativity. / Miao, Pengzi.
In: Communications in Mathematical Physics, Vol. 241, No. 1, 10.2003, p. 27-46.Research output: Contribution to journal › Article
}
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.
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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 -