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Static charged perfect fluid with the Weyl-Majumdar relation. (English) Zbl 1098.83544
Summary: Static charged perfect fluid distributions are studied. It is shown that if the norm of the timelike Killing vector and the electrostatic potential satisfy the Weyl-Majumdar relation, then the background spatial metric is the space of constant curvature, and the field equations reduce to a single non-linear partial differential equation. Furthermore, if a linear equation of state for the fluid is assumed, then this equation becomes a Helmholtz equation on the space of constant curvature. Some explicit solutions are given.

MSC:
83C20 Classes of solutions; algebraically special solutions, metrics with symmetries for problems in general relativity and gravitational theory
83C15 Exact solutions to problems in general relativity and gravitational theory
83C50 Electromagnetic fields in general relativity and gravitational theory
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