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arXiv · 1712.00785

Rigidity in vacuum under conformal symmetry

Gregory J. Galloway·Carlos Vega
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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.

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Gregory J. Galloway, Carlos Vega. 2017-12-03. Rigidity in vacuum under conformal symmetry. https://doi.org/10.1007/s11005-018-1079-7

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