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

Understand

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.