Rigidity in vacuum under conformal symmetry

2017/12/03 by Gregory J. Galloway, Carlos Vega · 1 citation
Physics and Astronomy · Mathematics · #gr-qc #math.DG

paper · pdf · doi:10.1007/s11005-018-1079-7

9 pages

arxiv created 2017/12/03 · arxiv updated 2018/05/09

Abstract

Moitvated in part by [3], 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.

Cited by

• Some remarks on conformal symmetries and Bartnik's splitting conjecture

Related

• Some remarks on conformal symmetries and Bartnik's splitting conjecture
• Conformal Killing Vectors in Spherically Symmetric, Inhomogeneous, Shear-free, Separable Metric Spacetimes
• A Constructive Approach to Infinitesimal Conformal Rigidity on Complex Hyperbolic Space
• Killing Initial Data on spacelike conformal boundaries
• Conformal Killing Vectors Of Plane Symmetric Four Dimensional Lorentzian Manifolds