Static Potentials on Asymptotically Flat Manifolds
Static Potentials on Asymptotically Flat Manifolds
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渐近平坦流形上的静势
DOI：
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发表时间：
2014
期刊：
影响因子：
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通讯作者：
Luen
中科院分区：
文献类型：
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作者：
P. Miao;Luen
我们考虑渐进平坦 3 流形上的静势是否可以具有延伸到无穷大的非空零集的问题。我们证明，如果度量是渐近史瓦西且质量非零，则不会发生这种情况。如果将渐近假设放宽到定义总质量的通常假设，我们就证明静态势在缩放范围内是唯一的，除非流形是平坦的。我们还提供了一些关于无边界、允许静势的完全渐近平坦 3 流形的刚性的讨论。
We consider the question whether a static potential on an asymptotically flat 3-manifold can have nonempty zero set which extends to the infinity. We prove that this does not occur if the metric is asymptotically Schwarzschild with nonzero mass. If the asymptotic assumption is relaxed to the usual assumption under which the total mass is defined, we prove that the static potential is unique up to scaling unless the manifold is flat. We also provide some discussion concerning the rigidity of complete asymptotically flat 3-manifolds without boundary that admit a static potential.