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A rigidity theorem for nonvacuum initial data

Gabor Etesi
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Abstract

In this note we prove a theorem on non-vacuum initial data for general relativity. The result presents a ``rigidity phenomenon'' for the extrinsic curvature, caused by the non-positive scalar curvature. More precisely, we state that in the case of asymptotically flat non-vacuum initial data if the metric has everywhere non-positive scalar curvature then the extrinsic curvature cannot be compactly supported.

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Gabor Etesi. 2002-01-21. A rigidity theorem for nonvacuum initial data. https://doi.org/10.1063/1.1421422

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