Charged Annular Disks and Reissner-Nordstr\"{o}m Type Black Holes from Extremal Dust

TL;DR

This paper analytically constructs a model of a charged black hole surrounded by an extremal dust annular disk, solving Einstein-Maxwell equations and employing Kelvin inversion, with all energy conditions satisfied.

Contribution

It introduces the first analytical superposition of a charged black hole with an extremal dust annular disk using a novel solution method.

Findings

Structures extend to infinity with finite total mass.

Energy conditions are satisfied in the models.

Reissner-Nordström black hole embedded at the disk center.

Abstract

We present the first analytical superposition of a charged black hole with an annular disk of extremal dust. In order to obtain the solutions, we first solve the Einstein-Maxwell field equations for sources that represent disk-like configurations of matter in confomastatic spacetimes by assuming a functional dependence among the metric function, the electric potential and an auxiliary function,which is taken as a solution of the Laplace equation. We then employ the Lord Kelvin Inversion Method applied to models of finite extension in order to obtain annular disks. The structures obtained extend to infinity, but their total masses are finite and all the energy conditions are satisfied. Finally, we observe that the extremal Reissner-Nordstr\"{o}m black hole can be embedded into the center of the disks by adding a boundary term in the inversion.