Symmetries and the Einstein-Maxwell field equations the null field case

Details Symmetries and the Einstein-Maxwell field equations the null field case Symmetries and the Einstein-Maxwell field equations the null field case

Jul 1976

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1976gregr...7..595w&link_type=abstract

General Relativity and Gravitation, Volume 7, Issue 7, pp.595-608

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This paper deals with space-times that satisfy the Einstein-Maxwell field equations in the presence of a perfect fluid, which may be charged. The electromagnetic field is assumed to be null. It is proved that if the space-time admits a group of isometrics then the fluid velocityu i, energy densityμ, pressurep, and charge densityɛ are invariant under the group. In addition, if the charge density is nonzero, the electromagnetic field tensorf ij is also invariant. On the other hand, examples of exact solutions are given which establish that ifɛ = 0, thenF ij is not necessarily invariant under the group. In the case of spherically symmetric space-times, however, in which the group of isometries acting isSO (3),f ij is invariant, independently of whether or notɛ is nonzero. This result leads to the conclusion that in a spherically symmetric space-time the field equations in question admit no solutions with non-trivial null electromagnetic field.

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