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On Killing vectors and invariance transformations of the Einstein–Maxwell equations

Published online by Cambridge University Press:  24 October 2008

M. L. Woolley
M. L. Woolley
Affiliation:
Astronomy Centre, University of Sussex
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Abstract

It is shown that, in a simply connected four dimensional Riemannian space, an arbitrary divergence-free vector generates a one-parameter group of point transformations which leaves Maxwell's equations unchanged. This result is used to show that, if the metric tensor of a simply connected vacuum Einstein–Maxwell space-time admits a group of motions which is also an invariance group of the electromagnetic field tensor, then there exists a one-parameter family of metric tensors all of which satisfy the Einstein–Maxwell equations with the invariant electromagnetic field as source.

Information

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 80 , Issue 2 , September 1976 , pp. 357 - 364
Copyright
Copyright © Cambridge Philosophical Society 1976

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References

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