Static Potentials on Asymptotically Flat Manifolds

Pengzi Miao, Luen Fai Tam

Research output: Contribution to journalArticlepeer-review

12 Scopus citations

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.

Original languageEnglish (US)
Pages (from-to)2239-2264
Number of pages26
JournalAnnales Henri Poincare
Volume16
Issue number10
DOIs
StatePublished - Oct 22 2015

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Nuclear and High Energy Physics
  • Mathematical Physics

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