### Abstract

The author considers source-free electromagnetic fields in spacetimes possessing a non-null Killing vector field, xi ^{a}. He further assumes that the electromagnetic field tensor, F_{ab}, is invariant under the action of the isometry group induced by xi ^{a}. It is then proved that whenever the two potentials associated with the electromagnetic field are functionally independent the entire content of Maxwell's equations is equivalent to the relation Del ^{a}T_{ab}=0. Since this relation is implied by Einstein's equation he argues that it is enough merely to solve Einstein's equation for these electrovac spacetimes because the relevant equations of motion will be automatically satisfied. It is also shown that for the exceptional case of functionally related potentials Del ^{a}T _{ab}=0 along with one of the relevant equations of motion implies that the complementary equation concerning the electromagnetic field is satisfied.

Original language | English |
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Article number | 010 |

Pages (from-to) | L167-L172 |

Journal | Classical and Quantum Gravity |

Volume | 10 |

Issue number | 9 |

DOIs | |

Publication status | Published - Dec 1 1993 |

### ASJC Scopus subject areas

- Physics and Astronomy (miscellaneous)

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## Cite this

*Classical and Quantum Gravity*,

*10*(9), L167-L172. [010]. https://doi.org/10.1088/0264-9381/10/9/010