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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.

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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