Asymptotically flat extensions of CMC Bartnik data

Armando J. Cabrera Pacheco, Carla Cederbaum, Stephen McCormick, Pengzi Miao

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6 Scopus citations

Abstract

Let g be a metric on the 2-sphere with positive Gaussian curvature and H be a positive constant. Under suitable conditions on (g, H), we construct smooth, asymptotically flat 3-manifolds M with non-negative scalar curvature, with outer-minimizing boundary isometric to and having mean curvature H, such that near infinity M is isometric to a spatial Schwarzschild manifold whose mass m can be made arbitrarily close to a constant multiple of the Hawking mass of . Moreover, this constant multiplicative factor depends only on (g, H) and tends to 1 as H tends to 0. The result provides a new upper bound of the Bartnik mass associated with such boundary data.

Original languageEnglish (US)
Article number105001
JournalClassical and Quantum Gravity
Volume34
Issue number10
DOIs
StatePublished - Apr 11 2017

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Keywords

  • Bartnik mass
  • constant mean curvature surfaces
  • Hawking mass
  • scalar curvature

ASJC Scopus subject areas

  • Physics and Astronomy (miscellaneous)

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