Static charged perfect fluid with the Weyl-Majumdar relation

Static charged perfect fluid distributions are studied. It is shown that if the norm of the timelike Killing vector and the electrostatic potential sa tisfy the Weyl-Majumdar relation, then the background spatial metric is the space of constant curvature, and the field equations reduce to a single no n-linear partial differential equation. Furthermore, if a linear equation o f state for the fluid is assumed, then this equation becomes a Helmholtz eq uation on the space of constant curvature. Some explicit solutions are give n.