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On the eigenvectors of the energy-momentum tensor in the Einstein–Maxwell theory

Published online by Cambridge University Press:  24 October 2008

M. L. Woolley
M. L. Woolley
Affiliation:
96 Highdown Road, Hove BN3 6EA, Sussex, England
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Abstract

It is shown that in the four-dimensional, source-free Einstein–Maxwell theory, four distinct orthogonal eigenvectors of the energy-momentum tensor may be obtained formally by the action of four projection operators on an almost arbitrary vector.

The extremal field, of the unified theory of Maxwell, Einstein and Rainich, is obtained explicitly in terms of eigenvectors of the energy-momentum tensor and the energy-momentum tensor itself, expressed in terms of eigenvectors, is seen to take on two equivalent forms. From this, a two-parameter group of Lorentz rotations, which leave the tetrad of eigenvectors unchanged, is deduced.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 74 , Issue 2 , September 1973 , pp. 281 - 288
Copyright
Copyright © Cambridge Philosophical Society 1973

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References

REFERENCES

(1)Misner, C. W. and Wheeler, J. A.Ann. Physics 2 (1957), 525–603.CrossRefGoogle Scholar
(2)Rainich, G. Y.Trans. Amer. Math. Soc. 27 (1925), 106.CrossRefGoogle Scholar
(3)Synge, J. L.Relativity, the special theory (North Holland, 1965).Google Scholar