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 $$p(r)=-\rho (r)/3$$ for the fluid in order to consider the closed ($$S_3$$) or the open ($$H_3$$) background spatial topology. Depending on the scales of the mass, spatial-curvature and charge parameters (K, $$R_0$$, Q), there are several types of solutions in $$S_3$$ and $$H_3$$ 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 $$S_3$$ outside the outer horizon due to the fluid. Both of the singularities can be accessed only by radial null rays