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On the analyticity of static vacuum solutions of Einstein's equations

Published online by Cambridge University Press:  24 October 2008

H. Müller zum Hagen
Affiliation:
King's College, London

Abstract

It is shown that around each point of a C3 static vacuum space-time there is a neighbourhood in which the metric is, in a certain suitable coordinate system, analytic. If two of these neighbourhoods overlap, then the transformation betweea these suitable coordinate systems is analytic (in the overlapping domain).

Type
Research Article
Copyright
Copyright © Cambridge Philosophical Society 1970

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References

REFERENCES

(1)Munkres, J.Elementary differential topology (Princeton University Press; Princeton, New Jersey, 1963).CrossRefGoogle Scholar
(2)Bers, L., John, F. and Schechter, M.Partial differential equations (Interscience Publishers; New York, London, Sydney, 1964).Google Scholar
(3)Bondi, H., Pirani, F. A. E. and Trautman, A. Brandeis Lectures: Lectures on general relativity (Prentice Hall, Inc. Englewood Cliffs, New Jersey, 1964).Google Scholar
(4)Dieudonné, J.Foundations of modern analysis (Academic Press; New York, London, 1960).Google Scholar
(5)Morrey, C. B.On the analyticity of the solutions of analytic non-linear elliptic systems of partial differential equations. Amer. J. Math. 80 (1958), 198237.CrossRefGoogle Scholar
(6)Cohn, P. M.Lie groups (Cambridge University Press; Cambridge, 1965).Google Scholar
(7)Müller zum Hagen, H. On the analyticity of stationary vacuum solutions of Einstein's equations. Proc. Cambridge Philos. Soc. (1970) to be published.Google Scholar