Rigidity in vacuum under conformal symmetry

Gregory J. Galloway, Carlos Vega

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

Abstract

Motivated in part by Eardley et al. (Commun Math Phys 106(1):137–158, 1986), in this note we obtain a rigidity result for globally hyperbolic vacuum spacetimes in arbitrary dimension that admit a timelike conformal Killing vector field. Specifically, we show that if M is a Ricci flat, timelike geodesically complete spacetime with compact Cauchy surfaces that admits a timelike conformal Killing field X, then M must split as a metric product, and X must be Killing. This gives a partial proof of the Bartnik splitting conjecture in the vacuum setting.

Original languageEnglish (US)
Pages (from-to)2285-2292
Number of pages8
JournalLetters in Mathematical Physics
Volume108
Issue number10
DOIs
StatePublished - Oct 1 2018

Keywords

  • Conformal symmetry
  • Lorentzian rigidity
  • Vacuum equations

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics

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