### 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 |
---|---|

Article number | 010 |

Journal | Classical and Quantum Gravity |

Volume | 10 |

Issue number | 9 |

DOIs | |

Publication status | Published - 1993 |

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### ASJC Scopus subject areas

- Physics and Astronomy(all)

### Cite this

**Maxwell fields in spacetimes admitting nonnull Killing vectors.** / Rácz, I.

Research output: Contribution to journal › Article

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TY - JOUR

T1 - Maxwell fields in spacetimes admitting nonnull Killing vectors

AU - Rácz, I.

PY - 1993

Y1 - 1993

N2 - 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, Fab, 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 aTab=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 aT ab=0 along with one of the relevant equations of motion implies that the complementary equation concerning the electromagnetic field is satisfied.

AB - 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, Fab, 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 aTab=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 aT ab=0 along with one of the relevant equations of motion implies that the complementary equation concerning the electromagnetic field is satisfied.

UR - http://www.scopus.com/inward/record.url?scp=36149037559&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=36149037559&partnerID=8YFLogxK

U2 - 10.1088/0264-9381/10/9/010

DO - 10.1088/0264-9381/10/9/010

M3 - Article

AN - SCOPUS:36149037559

VL - 10

JO - Classical and Quantum Gravity

JF - Classical and Quantum Gravity

SN - 0264-9381

IS - 9

M1 - 010

ER -