Where would the electric charge be stored on a black hole if one had charge?

Question

The charge for macroscopic objects is the accumulation of electrons. For elementary particles, charge is an intrinsic property. Since a black hole would have to accumulate electrons, they would cross the Schwarzschild radius $R_S$. The energy becoming a part of the spacetime warp. Where would the charge go or reside? Inside as well?

Answer 1

Charged Kerr solutions satisfy $\nabla_{a}F^{ab} = 0$, so there is no charge density anywhere in the spacetime. One can therefore presume that the charge lives in the singularity, if you're taking a deeply literal reading of GR.

If you take the perspective of modern black hole thermodynamics, the echoes of all of the properties of the black can be calculated from values measured on the horizon. So, in this picture, the black hole horizon, itself, carries the charge.