Static potentials on asymptotically flat manifolds

Abstract

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.

introduction revised; an outline of a space-time approach added

References in corpus (1)

• On Static n-body Configurations in Relativity

Cited by in corpus (6)

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• Mass, capacitary functions, and the mass-to-capacity ratio
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• Mean-stable surfaces in Static Einstein-Maxwell theory