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Distance to a focal point and singularity theorems with weak timelike convergence condition

Published online by Cambridge University Press:  01 March 2009

SEONG-HUN PAENG
SEONG-HUN PAENG*
Affiliation:
Department of Mathematics, Konkuk University, 1 Hwayang-dong, Gwangjin-gu, Seoul 143-701, Korea. e-mail: shpaeng@konkuk.ac.kr
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Abstract

In classical general relativity, the timelike convergence condition is Ric(v, v) ≥ 0 for every timelike vector v. But recent astronomical observations show that the timelike convergence condition does not hold. In this paper, we obtain an explicit upper bound of the volume form and the distance to a focal point (such as Hubble distance) along timelike geodesic with integrals of the negative part of Ricci curvature, which entails singularity theorems.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 146 , Issue 2 , March 2009 , pp. 475 - 487
Copyright
Copyright © Cambridge Philosophical Society 2008

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References

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