Test the horizon-charge attractor in three-dimensional simulations

Determine whether the integrated black-hole charge is insensitive to the azimuthal structure of the equatorial current sheet by testing the charge-attractor behavior in fully three-dimensional general-relativistic particle-in-cell simulations.

Background

The study uses axisymmetric, or 2.5D, general-relativistic particle-in-cell simulations, which exclude non-axisymmetric tearing and drift-kink instabilities and any azimuthal redistribution of charge. The authors argue that the measured charge may nevertheless be insensitive to these structures because it is an integral over the entire horizon.

A comparison with three-dimensional simulations is therefore needed to determine whether the common saturated charge found from initially neutral and Wald-charged black holes persists when the equatorial current sheet can fragment and develop fully non-axisymmetric dynamics.

References

Since the charge we measure is an integral over the whole horizon, it is plausibly insensitive to the sheet's azimuthal structure. Testing this expectation in 3D remains for future work.

— Charging of rotating black holes: kinetic simulations of black hole magnetospheres  (2609.16447 - Kološ et al., 15 Sep 2026) in Section 3.2, subsection “Initial conditions and numerical setup”