The structure of charged d-dimensional stars: Comparing different equations of state

In this work we review some of the general properties of static charged fluid in the context of the Einstein-Maxwell theory with cosmological term in four and higher dimensions. The metric is assumed to have a general form such that the geometry of the spatial section of the spacetime can be spherical, planar or hyperbolic. As first study we obtain the Tolman-Oppenheimer-Volkoff (TOV) equation, which describe the hydrostatic equilibrium, for a charged fluid in d-dimensional spacetime with cosmological constant for different geometries. In order to solve the resulting TOV equations, we need to provide an equation of state and an additional constraint for the charge density. For simplicity, the charge density is assumed to be proportional to the energy density, and we test such a set up for different charge fractions. We present and analyze numerical results showing the dependence of the star structure on the particular equation of state for two particular choices of equations of polytropic type.