Variational and rigidity properties of static potentials

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6 Scopus citations

Abstract

In this paper we study some global properties of static potentials on asymptotically flat 3-manifolds (M,g) in the nonvacuum setting. Heuristically, a static potential f represents the (signed) length along M of an irrotational timelike Killing vector field, which can degenerate on surfaces corresponding to the zero set of f. Assuming a suitable version of the null energy condition, we prove that a noncompact component of the zero set must be area minimizing. From this we obtain some rigidity results for static potentials that have noncompact zero set components, or equivalently, that are unbounded. Roughly speaking, these results show, at the pure initial data level, that 'boost-type' Killing vector fields can exist only under special circumstances.

Original languageEnglish (US)
Pages (from-to)163-183
Number of pages21
JournalCommunications in Analysis and Geometry
Volume25
Issue number1
StatePublished - 2017

ASJC Scopus subject areas

  • Analysis
  • Statistics and Probability
  • Geometry and Topology
  • Statistics, Probability and Uncertainty

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