Fluid black holes with electric field

We investigate the gravitational field of static perfect-fluid in the presence of electric field. We adopt the equation of state p(r) = - ρ(r) / 3 for the fluid in order to consider the closed (S₃) or the open (H₃) background spatial topology. Depending on the scales of the mass, spatial-curvature and charge parameters (K, R, Q), there are several types of solutions in S₃ and H₃ classes. Out of them, the most interesting solution is the Reisner–Norström type of black hole. Due to the electric field, there are two horizons in the geometry. There exists a curvature singularity inside the inner horizon as usual. In addition, there exists a naked singularity at the antipodal point in S₃ outside the outer horizon due to the fluid. Both of the singularities can be accessed only by radial null rays.