Static charged perfect fluid with the Weyl-Majumdar relation

TL;DR

This paper investigates static charged perfect fluid configurations under the Weyl-Majumdar relation, showing that the spatial metric is of constant curvature and deriving explicit solutions with a linear equation of state.

Contribution

It demonstrates that the Weyl-Majumdar relation simplifies the Einstein-Maxwell equations to a single PDE and provides explicit solutions for such fluid distributions.

Findings

Spatial metric is of constant curvature under the Weyl-Majumdar relation.

Field equations reduce to a Helmholtz equation with a linear equation of state.

Explicit solutions are constructed for the fluid configurations.

Abstract

Static charged perfect fluid distributions have been studied. It is shown that if the norm of the timelike Killing vector and the electrostatic potential have the Weyl-Majumdar relation, then the background spatial metric is the space of constant curvature, and the field equations reduces to a single non-linear partial differential equation. Furthermore, if the 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.