Fluid Black Holes with Electric Field

TL;DR

This paper explores static perfect-fluid black hole solutions with electric fields in closed and open spatial topologies, revealing multiple solution types including a Reissner-Nordström-like black hole with unique horizon and singularity structures.

Contribution

It introduces new solutions for fluid black holes with electric fields in curved backgrounds, highlighting the effects of topology and charge on horizon and singularity configurations.

Findings

Existence of multiple solution types depending on parameters.

Presence of two horizons and a curvature singularity.

Naked singularity at antipodal point outside the outer horizon.

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.