Solution of the Einstein–Maxwell equations with anisotropic negative pressure as a potential model of a dark energy star

Abstract

We have obtained a new class of solutions for the Einstein–Maxwell field equations for static spherically symmetric space–times by considering the negative anisotropic pressures, which represents a potential model of a dark energy star. We take the equation of state pr = −ρ, where pr is the radial pressure and ρ is the density. We have also checked that for these solutions metric coefficients, mass density, radial pressure, transverse pressure, electric field, and current density are well defined for suitable values of the parameters involved in the solution. These exact solutions can be used to develop models of dark energy stellar interiors satisfying all physical constraints except for the causality condition, which cannot be satisfied for the equation of state considered here, and which is arguably not an applicable physical constraint for dark matter–energy.