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Conformal deformations, Ricci curvature and energy conditions on globally hyperbolic spacetimes

Published online by Cambridge University Press:  24 October 2008

John K. Beem  and
Paul E. Ehrlich
John K. Beem
Affiliation:
University of Missouri, Columbia, Mo. 65201
Paul E. Ehrlich
Affiliation:
University of Missouri, Columbia, Mo. 65201
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Abstract

We consider globally hyperbolic spacetimes (M, g) of dimension ≥ 3 satisfying the curvature condition Ric (g) (v, v) ≥ 0 for all non-spacelike tangent vectors v in TM. This curvature condition arises naturally as an energy condition in cosmology. Suppose (M, g) admits a smooth globally hyperbolic time function h: M → such that for some t0, the Cauchy surface h−1(t0) satisfies the strict curvature condition Ric (g) (v, v) > 0 for all non-spacelike v attached to h−1(t0). Then M admits a metric g′ conformal to g satisfying the strict curvature condition Ric (g′) (v, v) > 0 for all non-spacelike v in TM. If the curvature and strict curvature conditions are restricted to null vectors, the analogous result may be obtained. Similar results may also be obtained for the scalar curvature in dimension ≥ 2 and for non-positive Ricci curvature.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 84 , Issue 1 , July 1978 , pp. 159 - 175
Copyright
Copyright © Cambridge Philosophical Society 1978

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References

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