Killing vector fields and the Einstein-Maxwell field equations with perfect fluid source

This paper is concerned with space-times that satisfy the Einstein-Maxwell field equations in the presence of a perfect fluid, which may be charged. We consider the following question. Suppose that the space-time admits a group of motions (isometries), i.e., that the metric is invariant under a group of transformations. Does it follow that the quantities that describe the source, i.e., the electromagnetic field tensorF _ij, the charge densityε, and the four-velocityu ⁱ, energy densityμ, and pressurep of the fluid, are invariant under the group? It is found that the behavior of these quantities under the group is strongly restricted. In particular in the case of the three-dimensional special orthogonal groupSO(3), which arises in the case of spherically symmetric space-times, it is found that the source quantities are invariant. On the other hand, it is established that there exist groups under whichF _ij is not necessarily invariant. The above question is also considered for the case of homothetic motions.