In the magnetically arrested disk (MAD) regime of black hole accretion, magnetic flux accumulating on the event horizon was found in a decade of general relativistic magnetohydrodynamic (GRMHD) simulations to saturate at a normalized value of order 50, capping the efficiency of spin-energy extraction by the Blandford–Znajek process at roughly 140% of the accreted rest-mass energy. Nathanail (2026, arXiv:2602.22824) reported high-resolution 3D GRMHD simulations of a rapidly spinning black hole in which weakly magnetized initial tori with poloidal magnetic flux enhanced at the inner edge drive extreme 'super-MAD' states: the inner accretion flow is displaced for more than 10,000 gravitational times in two of the three extreme models, and in the most extreme model accretion is halted over the full azimuthal extent during an episode of about 3,000 gravitational times, the equatorial magnetospheric radius is pushed to roughly 3–5 gravitational radii, the normalized horizon flux far exceeds the canonical saturation limit, and the time-averaged jet efficiency exceeds 170 times the accreted rest-mass energy rate. The open problem, stated explicitly by the source as future work, is whether such extreme accretion-suppressed magnetospheres are persistent quasi-steady regimes or transient episodes; whether configurations sustaining magnetospheric radii beyond about 5 gravitational radii, or such radii for much longer times, exist; and whether the required large-scale poloidal flux can be supplied astrophysically by accretion dynamos or naturally accreted stellar/tidal-disruption flux rather than pre-existing external flux. No independent confirmation or refutation of these questions is known; adjacent results on standard MADs, flux-eruption physics, and magnetic-flux supply do not settle these questions, which remain open.

Background

A rotating (Kerr) black hole can act as an electromagnetic engine: in the Blandford–Znajek (BZ) process, magnetic field lines threading the event horizon, twisted by frame dragging, extract rotational energy and launch relativistic jets (Blandford & Znajek 1977). The fuel is normally accreting gas, but the field itself can choke the supply. Igumenshchev (2008) showed in MHD simulations that a sufficiently strong vertical field halts the inner disk at a magnetospheric radius, forming a magnetically arrested disk (MAD); Tchekhovskoy, Narayan & McKinney (2011) found that in this state the normalized horizon flux ϕBH=ΦBH/M˙\phi_{\rm BH}=\Phi_{\rm BH}/\sqrt{\dot M} saturates at ϕBH≈50\phi_{\rm BH}\approx 50 (with ΦBH\Phi_{\rm BH} the horizon magnetic flux and M˙\dot M the mass accretion rate; the saturation value ≈50\approx 50 is quoted in Gaussian units — in the Heaviside–Lorentz units used by Nathanail 2026 it corresponds to 50/4π≈1450/\sqrt{4\pi}\approx 14) and that accretion proceeds through magnetized Rayleigh–Taylor-type interchange instabilities rather than stopping, giving time-averaged jet efficiencies η=Pjet/M˙c2≈1.4\eta=P_{\rm jet}/\dot M c^2\approx 1.4 — that is, jet power about 140% of the accreted rest-mass energy, the excess drawn from spin. McKinney, Tchekhovskoy & Blandford (2012) and Narayan et al. (2022), the latter averaging over 50,000–100,000 gravitational times tg=rg/ct_{\rm g}=r_{\rm g}/c (where rg=GM/c2r_{\rm g}=GM/c^2), confirmed this saturation picture across spins. MADs also produce quasi-periodic flux eruption events — expulsions of horizon flux by plasmoid-mediated reconnection (Ripperda et al. 2022) — which are the leading model for infrared and X-ray flares of Sgr A* (Antonopoulou, Loules & Nathanail 2025). The interest in pushing beyond this regime is observational: in powerful blazars the jet power can exceed the accretion-disk luminosity by factors of 10–100 or more (Ghisellini et al. 2014), and Blandford & Globus (2022) proposed theoretically that a highly magnetized 'ergomagnetosphere' could eject most of the supplied gas while the black hole spin powers both jet and outflow. Cho & Narayan (2025), surveying initial rotational-to-magnetic energy ratios, showed that strongly magnetized tori (plasma-β\beta, the gas-to-magnetic-pressure ratio, of order 1) produce violent variability with jet efficiency swinging by three orders of magnitude, but not a globally suppressed, quasi-steady state. Against this backdrop, Nathanail (2026) performed 3D GRMHD simulations with the BHAC code of a Kerr black hole with dimensionless spin a∗=0.9375a_*=0.9375, initializing a weakly magnetized, radially infalling torus threaded by a density-following poloidal loop field (net flux zero, but with enhanced flux at the inner edge; initial plasma-β=2p/B2\beta=2p/B^2 of 7–100) and varying the initial magnetic pressure over four models (MAD.S.100, .26, .13, .7, in order of increasing magnetization) at resolution 384×192×192384\times192\times192. The standard model behaves like a canonical MAD, but the three extreme models develop 'super-MAD' states: in models MAD.S.26 and MAD.S.13 the accumulation of magnetic flux produces a long-lived displacement of the inner accretion flow, with the equatorial magnetospheric radius rmagr_{\rm mag} — defined by the equatorial magnetization σ=B2/ρc2=1\sigma=B^2/\rho c^2=1 contour — remaining near 3 rg3\,r_{\rm g} for more than 10,000 tgt_{\rm g}, while accretion continues through narrow, non-axisymmetric instabilities (model MAD.S.13 is markedly more variable, with temporary suppressions of about 100–200 tgt_{\rm g} and horizon accretion-rate fluctuations of up to three orders of magnitude), and in the most extreme case (MAD.S.7) the system undergoes a stronger but shorter-lived episode of about 3,000 tgt_{\rm g} in which the magnetosphere expands to roughly 5 rg5\,r_{\rm g} and accretion is temporarily halted over the full azimuthal extent; the normalized horizon flux exceeds the canonical saturation limit by large factors, and the time-averaged jet efficiency reaches η≈8\eta\approx 8 (MAD.S.26) and η>170\eta>170 (MAD.S.7), with instantaneous values up to about 400 during the suppressed phase (in the source, PjetP_{\rm jet} is measured on a sphere at 50 rg50\,r_{\rm g} and the quoted averages are taken over 3,000–10,000 tgt_{\rm g} windows). The familiar quasi-periodic flux eruptions are replaced by large-scale magnetic reorganizations spanning wide azimuthal ranges, whose statistics are not characterized. The author's own robustness tests cover floor treatment and primitive-variable inversion at reduced resolution, but only one spin is simulated, the outer boundary fixes the feeding reservoir, and the run durations are finite — leaving the physical status of these states undetermined.

Problem Statement

Determine whether the extreme, globally accretion-suppressed magnetospheric configurations ('super-MAD' states) realized in the general relativistic magnetohydrodynamic (GRMHD) simulations of Nathanail (2026) are genuine astrophysical regimes or finite transients, and under what conditions nature can realize them. Concretely: (1) establish whether a globally accretion-suppressed configuration — in the existing runs, a mean equatorial magnetospheric radius ⟨rmag⟩\langle r_{\rm mag}\rangle near 3 rg3\,r_{\rm g} maintained for more than 10,000 tgt_{\rm g} in models MAD.S.26 and MAD.S.13, with accretion continuing through narrow, non-axisymmetric channels (the horizon mass-accretion rate M˙\dot M drops to very low but not identically zero values and can fluctuate by up to three orders of magnitude, so 'halted' is convention-dependent), and a temporary halt of accretion over the full azimuthal extent at ⟨rmag⟩≈5 rg\langle r_{\rm mag}\rangle\approx 5\,r_{\rm g} during an episode of about 3,000 tgt_{\rm g} in model MAD.S.7, where tg=rg/ct_{\rm g}=r_{\rm g}/c is the gravitational time and rg=GM/c2r_{\rm g}=GM/c^2 the gravitational radius — is a long-lived quasi-steady state that persists on astrophysical timescales or a transient episode of limited duration, where a suppressed state counts as long-lived if it is maintained for at least an order of magnitude beyond the durations already demonstrated (≳105 tg\gtrsim10^{5}\,t_{\rm g}) or if an explicit dynamical-stability or analytic argument establishes that the suppression is not a precursor, and as transient otherwise, given that runs of these lengths cannot distinguish eventual saturation from precursor behavior; (2) determine whether configurations exist that sustain a mean equatorial magnetospheric radius ⟨rmag⟩\langle r_{\rm mag}\rangle — the radius at which the equatorial magnetization σ=B2/ρc2\sigma=B^2/\rho c^2 (magnetic energy density over rest-mass energy density, with ρ\rho the rest-mass density) reaches unity — beyond roughly 5 rg5\,r_{\rm g}, or persist at such radii for the same long-lived duration defined in (1) (at least an order of magnitude beyond the durations already demonstrated, ≳105 tg\gtrsim10^{5}\,t_{\rm g}); and (3) establish whether the required large-scale poloidal flux can be supplied astrophysically — by turbulent accretion dynamos or flux naturally accreted in stellar tidal disruptions and related events — or whether super-MAD states can only arise from externally provided, pre-existing flux. These three determinations are the complete required answer and jointly serve one objective: fixing the true limits of Blandford–Znajek energy extraction — the process by which magnetic field lines threading a spinning black hole's event horizon, twisted by frame dragging, extract its rotational energy — by establishing whether the canonical MAD saturation (ϕBH≈50\phi_{\rm BH}\approx 50 normalized horizon magnetic flux, η≈1.4\eta\approx 1.4 jet efficiency relative to the accreted rest-mass energy rate) is a physical ceiling or the artifact of a limited regime; the conditions under which jet efficiencies of tens to hundreds of times the accreted rest-mass energy rate can be realized in nature are exactly the persistence, magnetospheric-radius, and flux-supply requirements established by determinations (1)-(3).

References

  1. Nathanail, A. 2026, 'Black hole Limits Redefined: Extreme Efficiency in Black Hole Jets', arXiv:2602.22824, https://arxiv.org/abs/2602.22824
  2. Blandford, R. D., & Znajek, R. L. 1977, 'Electromagnetic extraction of energy from Kerr black holes', Mon. Not. R. Astron. Soc. 179, 433, doi:10.1093/mnras/179.3.433, https://doi.org/10.1093/mnras/179.3.433
  3. Igumenshchev, I. V. 2008, 'Magnetically Arrested Disks and the Origin of Poynting Jets: A Numerical Study', Astrophys. J. 677, 317, arXiv:0711.4391, doi:10.1086/529025, https://doi.org/10.1086/529025
  4. Tchekhovskoy, A., Narayan, R., & McKinney, J. C. 2011, 'Efficient generation of jets from magnetically arrested accretion on a rapidly spinning black hole', Mon. Not. R. Astron. Soc. 418, L79, arXiv:1108.0412, doi:10.1111/j.1745-3933.2011.01147.x, https://doi.org/10.1111/j.1745-3933.2011.01147.x
  5. McKinney, J. C., Tchekhovskoy, A., & Blandford, R. D. 2012, 'General relativistic magnetohydrodynamic simulations of magnetically choked accretion flows around black holes', Mon. Not. R. Astron. Soc. 423, 3083, arXiv:1201.4163, doi:10.1111/j.1365-2966.2012.21074.x, https://doi.org/10.1111/j.1365-2966.2012.21074.x
  6. Narayan, R., Chael, A., Chatterjee, K., Ricarte, A., & Curd, B. 2022, 'Jets in magnetically arrested hot accretion flows: geometry, power, and black hole spin-down', Mon. Not. R. Astron. Soc. 511, 3795, arXiv:2108.12380, doi:10.1093/mnras/stac285, https://doi.org/10.1093/mnras/stac285
  7. Blandford, R., & Globus, N. 2022, 'Ergomagnetosphere, ejection disc, magnetopause in M87 - I. Global flow of mass, angular momentum, energy, and current', Mon. Not. R. Astron. Soc. 514, 5141, arXiv:2204.11995, doi:10.1093/mnras/stac1682, https://doi.org/10.1093/mnras/stac1682
  8. Ghisellini, G., Tavecchio, F., Maraschi, L., Celotti, A., & Sbarrato, T. 2014, 'The power of relativistic jets is larger than the luminosity of their accretion disks', Nature 515, 376, arXiv:1411.5368, doi:10.1038/nature13856, https://doi.org/10.1038/nature13856
  9. Cho, H., & Narayan, R. 2025, 'Variability in Black Hole Accretion: Dependence on Rotational and Magnetic Energy Balance', Astrophys. J. 991, 89, arXiv:2507.13441, doi:10.3847/1538-4357/adf8d3, https://doi.org/10.3847/1538-4357/adf8d3
  10. Ripperda, B., Liska, M., Chatterjee, K., Musoke, G., Philippov, A. A., Markoff, S. B., Tchekhovskoy, A., & Younsi, Z. 2022, 'Black Hole Flares: Ejection of Accreted Magnetic Flux through 3D Plasmoid-mediated Reconnection', Astrophys. J. Lett. 924, L32, arXiv:2109.15115, doi:10.3847/2041-8213/ac46a1, https://doi.org/10.3847/2041-8213/ac46a1
  11. Antonopoulou, E., Loules, A., & Nathanail, A. 2025, 'Magnetically arrested disk flux eruption events to describe SgrA* flares', Astron. Astrophys. 696, A10, arXiv:2501.07521, doi:10.1051/0004-6361/202453456, https://doi.org/10.1051/0004-6361/202453456
  12. Loules, A., Nathanail, A., & Contopoulos, I. 2026, 'The azimuthal structure of magnetically arrested disks during flux eruption events', Astron. Astrophys. 710, A37, arXiv:2604.14313, doi:10.1051/0004-6361/202555642, https://doi.org/10.1051/0004-6361/202555642
  13. Ricarte, A., Chavez, E., O, F., & Protopapas, P. 2026, 'Identifying Observational Signatures of Flux Eruption Events in Supermassive Black Hole Accretion Flows with Machine Learning', arXiv:2606.28603, https://arxiv.org/abs/2606.28603
  14. Glaser, F., Fromm, C. M., Mizuno, Y., Kadler, M., & Mannheim, K. 2026, 'The magnetic filling in magnetically arrested accretion disk simulations and its impact on the jet in M87', arXiv:2602.20893, https://arxiv.org/abs/2602.20893
  15. Wong, G. N., & Stone, J. M. 2026, 'The SANE, the MAD, and the Chimera', arXiv:2607.07784, https://arxiv.org/abs/2607.07784
  16. Tchekhovskoy, A., Metzger, B. D., Giannios, D., & Kelley, L. Z. 2014, 'Swift J1644+57 gone MAD: the case for dynamically important magnetic flux threading the black hole in a jetted tidal disruption event', Mon. Not. R. Astron. Soc. 437, 2744, arXiv:1301.1982, doi:10.1093/mnras/stt2085, https://doi.org/10.1093/mnras/stt2085
  17. Dhang, P., Bai, X.-N., & White, C. J. 2023, 'Magnetic Flux Transport in Radiatively Inefficient Accretion Flows and the Pathway toward a Magnetically Arrested Disk', Astrophys. J. 944, 182, arXiv:2208.02269, doi:10.3847/1538-4357/acb534, https://doi.org/10.3847/1538-4357/acb534
  18. Kwan, T. M., Dai, L., & Tchekhovskoy, A. 2023, 'The Effects of Gas Angular Momentum on the Formation of Magnetically Arrested Disks and the Launching of Powerful Jets', Astrophys. J. Lett. 946, L42, arXiv:2211.12726, doi:10.3847/2041-8213/acc334, https://doi.org/10.3847/2041-8213/acc334