Rigidity in vacuum under conformal symmetry |
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Authors: | Gregory J. Galloway Carlos Vega |
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Affiliation: | 1.Department of Mathematics,University of Miami,Coral Gables,USA;2.Department of Mathematics,Binghamton University SUNY,Binghamton,USA |
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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. |
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