Isometric motions of a perfect charged fluid

Abstract

Space-times with perfect charged fluids as sources, that admit groups G_r of isometric motions, are investigated. It is assumed that the velocity vector of the fluid is collinear to the timelike Killing vector ξⁱ of group G_r. It is shown that the macroscopic motion of a perfect charged fluid can occur only in the direction of such a Killing vector ξⁱ that defines an operator in an invariant subgroup or, in particular, an operator of the center of the group. Parametric representations of the generalized equations of state for the pressure p, the energy density of the fluid, ρ, and the electric charge density σ are established. All these quantities are functions of the norm of the Killing vector ξⁱ and the projection of the 4-potential of the electromagnetic field onto this vector ξⁱ. In the approximation of the weak field in the coordinate system where ξⁱ=δ ⁱ₄ , these functional dependences imply that p, ρ, and σ are functions of Newtonian and electrostatic potentials.