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Spherically symmetric space-time of class one and electromagnetism

Published online by Cambridge University Press:  24 October 2008

S. N. Pandey  and
I. D Kansal
S. N. Pandey
Affiliation:
Department of Mathematics, University of Roorkee, Roorkee (India)
I. D Kansal
Affiliation:
Department of Mathematics, University of Roorkee, Roorkee (India)
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Abstract

It is well known that a spherically symmetric space-time is, in general, of class two. A necessary and sufficient condition for a spherically symmetric space-time to be of class one has been obtained in terms of the Riemann curvature tensor. By means of a transformation property of s.s. space-time, three distinct cases are shown to exist. The incompatibility of class one spherically symmetric space-times with Rainich algebraic conditions is established in these three cases. It is concluded that spherically symmetric electromagnetic fields cannot be embedded in a flat space of 5-dimensions.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 64 , Issue 3 , July 1968 , pp. 757 - 764
Copyright
Copyright © Cambridge Philosophical Society 1968

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References

REFERENCES

(1)Singh, K. P. and Pandey, S. N.Riemannian fourfolds of class one and gravitation. Proc. Nat. Inst. Sci. India 26 Part A (1960), 665–672.Google Scholar
(2)Thomas, T. Y.Riemannian spaces of class one and their characterization. Acta. Math. 67 (1963), 169–211.CrossRefGoogle Scholar
(3)Karmarkar, K. R.Gravitational metrics of spherical symmetry and class one. Proc. Indian Acad. Sci. 27 (1948), 56.CrossRefGoogle Scholar
(4)Witten, L.Gravitation: an introduction to current research, p. 385 (John Wiley and Sons, 1962).Google Scholar
(5)Narlikar, V. V. and Vaidya, P. C.Non-static electromagnetic fields with spherical symmetry. Proc. Nat. Inst. Sci. India 14 (1948), 53.Google Scholar
(6)Nordstrom, G.Calculation of some special cases in Einstein's theory of gravitation. Nederl. Akad. Wetensch. Proc. Ser A, 21 (1918), 68.Google Scholar
(7)Eisenhart, L. P.Riemmannian Geometry p. 200. (Princeton, 1960).Google Scholar
(8)Tolman, R. C.Relativity Thermodynamics and Cosmology, p. 272. (Oxford, 1934).Google Scholar