A rigidity theorem for nonvacuum initial data
arXiv:gr-qc/0101006 · doi:10.1063/1.1421422
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.
This is an extended and published version: LaTex, 10 pages, no figures