On Existence of Static Metric Extensions in General Relativity
On Existence of Static Metric Extensions in General Relativity
复制标题
论广义相对论中静态度量扩张的存在性
DOI：
10.1007/s00220-003-0925-2
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发表时间：
2003
影响因子：
2.4
通讯作者：
P. Miao
中科院分区：
文献类型：
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作者：
P. Miao
受广义相对论中准定域质量问题的启发，我们研究了R。巴特尼克[4]。我们证明了，对于<$B1上的任何度量，只要它足够接近于欧几里德度量并且具有反射不变的边界数据，在M=<$3 <$B1中总是存在一个渐近平坦和标量平坦的静态度量扩张，使得它满足<$B1上的Bartnik几何边界条件[4]。
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 ¯B1 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 [4] on ∂B1.