Charging of rotating black holes: kinetic simulations of black hole magnetospheres
Abstract
Whether a rotating black hole (BH) immersed in an external magnetic field charges up to the Wald value QW=2aMB, where M and a are the BH mass and spin parameter, and B is the strength of the external field, is a long-standing open question in BH electrodynamics, with consequences for charge separation, particle acceleration and the structure of BH magnetospheres. We address it with axisymmetric general-relativistic particle-in-cell simulations performed with GRZeltron, including self-consistent pair creation. For representative values of the BH spin, we evolve the same asymptotically uniform Wald field from two opposite initial horizon charges, Q0=0 and Q0=QW, and track the accumulated charge through the BH horizon. We find that both branches relax within a few tens of gravitational times to the same saturated charge value. Thus, the equilibrium is a dynamical attractor of the kinetic magnetosphere rather than a memory of the initial data. The attractor lies well below QW, at ξeq≡ Qeq/QW≈ 0.3 for a≲0.7, then falling almost to ξeq≈0 for large spins a≈1. We derive an analytic expression for ξeq by requiring equal magnetic fluxes through the horizon associated with positive and negative charges, and find its spin dependence to be in agreement with the simulations. The charge state of an astrophysical BH is therefore driven by kinetic plasma processes, and the Wald charge is an upper bound, not a general equilibrium value. Since ξeq<1, charging does not quench the horizon-infinity potential drop that powers energy-extraction processes such as the Blandford-Znajek mechanism.
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BibTeX
@misc{kolos2026charging,
title = {{Charging of rotating black holes: kinetic simulations of black hole magnetospheres}},
author = {Martin Kološ and Farukh Abdulkhamidov and Arman Tursunov and Jorge A Rueda and Benoît Cerutti},
howpublished = {HAL},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.16447},
eprint = {2609.16447},
archivePrefix = {arXiv},
url = {https://hal.science/hal-05773288v1},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Charging of rotating black holes: kinetic simulations of black hole magnetospheres
AU - Martin Kološ
AU - Farukh Abdulkhamidov
AU - Arman Tursunov
AU - Jorge A Rueda
AU - Benoît Cerutti
PY - 2026
DA - 2026/09/15
PB - HAL
DO - 10.48550/arxiv.2609.16447
UR - https://hal.science/hal-05773288v1
AB - Whether a rotating black hole (BH) immersed in an external magnetic field charges up to the Wald value Q_W=2aMB, where M and a are the BH mass and spin parameter, and B is the strength of the external field, is a long-standing open question in BH electrodynamics, with consequences for charge separation, particle acceleration and the structure of BH magnetospheres. We address it with axisymmetric general-relativistic particle-in-cell simulations performed with GRZeltron, including self-consistent pair creation. For representative values of the BH spin, we evolve the same asymptotically uniform Wald field from two opposite initial horizon charges, Q_0=0 and Q_0=Q_W, and track the accumulated charge through the BH horizon. We find that both branches relax within a few tens of gravitational times to the same saturated charge value. Thus, the equilibrium is a dynamical attractor of the kinetic magnetosphere rather than a memory of the initial data. The attractor lies well below Q_W, at ξ_eq≡ Q_eq/Q_W≈ 0.3 for a≲0.7, then falling almost to ξ_eq≈0 for large spins a≈1. We derive an analytic expression for ξ_eq by requiring equal magnetic fluxes through the horizon associated with positive and negative charges, and find its spin dependence to be in agreement with the simulations. The charge state of an astrophysical BH is therefore driven by kinetic plasma processes, and the Wald charge is an upper bound, not a general equilibrium value. Since ξ_eq<1, charging does not quench the horizon-infinity potential drop that powers energy-extraction processes such as the Blandford-Znajek mechanism.
ER -