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On the differentiability of space-time

Published online by Cambridge University Press:  24 October 2008

C. J. S. Clarke
C. J. S. Clarke
Affiliation:
University of York
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Abstract

It is shown that the differentiability of a space-time is implied by that of its Riemann tensor, assuming a priori only boundedness of the first derivations of the metric. Consequently all the results on space-time singularities proved in earlier papers by the author hold true in C2− space-times.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 81 , Issue 2 , March 1977 , pp. 279 - 282
Copyright
Copyright © Cambridge Philosophical Society 1977

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References

REFERENCES

(1)Clarke, C. J. S.The classification of singularities. General Relativity and Gravitation 6 (1975), 35–40.CrossRefGoogle Scholar
(2)Clarke, C. J. S.Singularities in globally hyperbolic space-time. Comm. Math. Phys. 41 (1975), 65–78.CrossRefGoogle Scholar
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(6)Gel'Fand, I. M. & Shilov, G. E.Generalised Functions, vol. I. (New York: Academic Press, 1964.)Google Scholar