Abstract
Einstein’s field equations which include electromagnetism are investigated when the metric admits a timelike Killing motion and the source is a charged perfect fluid under isometric motion. It is shown that the pressure must necessarily be a function of the electrostatic and gravitational potentials. A class of solutions is found under the following simplifying assumptions: (i) The pressure is a constant, (ii) the Lorentz force vanishes, and (iii) the magnetic and twist potentials are functionally related. In this class the ratio of σ/(ρ+3p) is a constant and this resembles an equilibrium condition. Finally a four-parameter group (maximal) is supplied which can generate new solutions of this class.
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