A rigidity theorem for nonvacuum initial data

Details A rigidity theorem for nonvacuum initial data A rigidity theorem for nonvacuum initial data

2000-12-31

arxiv.org/abs/gr-qc/0101006v3

Journ. Math. Phys. 43(2) 554-562 (2002)

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

This is an extended and published version: LaTex, 10 pages, no figures

Scientific paper

10.1063/1.1421422

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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