Fluid Black Holes with Electric Field

Abstract

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-Norstr\"om 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.