Astrophysical viability of the magnetic Penrose process: efficiency in realistic non-uniform, plasma-filled magnetospheres and superspinar-versus-black-hole diagnostics

The magnetic Penrose process (MPP) — energy extraction from a rotating black hole by charged particle fragments coupling to an ambient magnetic field in the ergosphere — predicts efficiencies exceeding 100% already at milli-Gauss fields, and, in the exact magnetized-Kerr computation of Chakraborty, Patil and Akash (2024), a maximum at spin $a_* \approx 0.786$, suppression to zero for ultra-strong fields $B > B_p \approx 0.36M^{-1}$ for black holes, and the opposite, monotonically increasing efficiency for Kerr superspinars. All quantitative MPP results hold for test particles in an asymptotically uniform magnetic field on the non-asymptotically-flat magnetized Kerr electrovacuum. The open problem is to determine whether these predictions survive in a realistic magnetosphere — spatially varying fields, collective plasma effects, pair production, radiative losses — and whether the channel yields concrete observable signatures, in particular signatures that would distinguish a Kerr superspinar from a Kerr black hole.

Background

The Penrose process extracts rotational energy from a rotating (Kerr) black hole: inside the ergosphere, the region where spacetime dragging forbids any observer from remaining at rest with respect to infinity, a particle can split into fragments, one of which falls into the hole on an orbit of negative energy as measured from infinity, so the escaping fragment carries away more energy than the incoming particle had. For a Kerr black hole with dimensionless spin parameter $a_*$ (angular momentum per unit gravitational mass, $0 \le a_* \le 1$), the efficiency $\eta = E_{out}/E_{in}$ of this purely mechanical process is at most 20.7%, attained at $a_* = 1$.

The magnetic Penrose process (MPP) revives the mechanism. When the splitting fragment is electrically charged and the hole sits in an ordered magnetic field, the electromagnetic coupling term $qA_t$ in the conserved particle energy lets a fragment reach a negative-energy state without the severe relative-velocity constraint of the original process, and the efficiency can exceed 100% (Wagh, Dhurandhar and Dadhich 1985), for electrons around a stellar-mass hole already at a milli-Gauss field (Dadhich et al. 2018). Field strength is conventionally quoted in geometrized units ($G = c = 1$) as the product $BM$: $BM \ll 1$ is a weak test field that solves Maxwell's equations on an undisturbed Kerr background (the Wald field), while $B \sim O(M^{-1})$ is ultra-strong — the field's own stress-energy distorts the geometry and an exact electrovacuum solution, such as the magnetized Kerr (Ernst-type) spacetime, is required. In these units $B \approx 0.2M^{-1}$ corresponds to roughly $10^{10}$ G for a $10^9$ solar-mass hole and $10^{18}$ G for a near-solar-mass hole, whereas fields actually inferred near event horizons are far weaker (about 1–30 G for M87* and Sgr A*).

Chakraborty, Patil and Akash (2024) derived the exact MPP efficiency in the magnetized Kerr spacetime, valid from the weak-field to the ultra-strong regime and for both Kerr black holes and Kerr superspinars — hypothetical objects with $a_* > 1$ that violate the Kerr (cosmic-censorship) bound but are presumed cut off at a small radius $R_s$ (taken as $10^{-3}M$ as a conservative proxy) where quantum-gravity effects resolve the classical ring singularity. Their key results: (i) for black holes the efficiency rises with $B$ to a peak of order $10^{22}$% at the threshold $B_p \approx 0.36M^{-1}$ and is driven to zero for $B > B_p$; (ii) the peak efficiency occurs at $a_* \approx 0.786$ and decreases toward $a_* = 1$, a manifestation of the gravitational Meissner effect, the tendency of near-extremal Kerr spacetimes to expel ambient magnetic flux; (iii) superspinars show the opposite trend, with efficiency increasing monotonically into the ultra-strong regime, so that the superspinar efficiency exceeds the black-hole efficiency there.

All of these quantitative results hold in the test-particle limit in an asymptotically uniform magnetic field on the non-asymptotically-flat magnetized Kerr electrovacuum. Real black-hole magnetospheres are plasma-filled and spatially varying, and the standard plasma-level extraction channel, the Blandford–Znajek (BZ) mechanism — rotational energy extracted through currents and twisted field lines in a force-free magnetosphere, a plasma state in which inertial forces are negligible — is the accepted engine of relativistic jets. How the particle-level MPP picture relates to the plasma-level BZ picture has been debated (Dadhich 2012 argues BZ is contained in MPP in the high-field limit; Lasota et al. 2014 argue that in force-free extraction the negative-energy carrier is the electromagnetic field itself, a generalized Penrose process). Whether the striking test-particle MPP predictions survive contact with plasma physics, and whether they yield observable signatures, is the open problem.

Problem Statement

Determine whether the magnetic Penrose channel of energy extraction from Kerr collapsed objects — with its striking test-particle predictions: efficiency exceeding 100% already at milli-Gauss fields, a maximum at $a_* \approx 0.786$ from the gravitational Meissner effect, suppression to zero for $B > B_p \approx 0.36M^{-1}$ in the case of black holes, and the opposite, monotonically increasing efficiency for superspinars — survives the idealizations under which it was derived (test particles in an asymptotically uniform magnetic field on the non-asymptotically-flat magnetized Kerr electrovacuum), and what observable signatures the channel produces. The common scientific objective is the astrophysical viability and observable content of the magnetic Penrose process; the following linked results jointly support it.

1. Non-uniform fields. Compute the MPP efficiency for at least one explicitly specified spatially varying external magnetic field (for example a dipolar or plasma-current-supported configuration) around a Kerr black hole, quantifying how the efficiency and the suppression threshold $B_p$ shift relative to the exact uniform-field results.

2. Plasma environment. Assess how collective plasma effects, pair loading, and radiative losses modify the test-particle efficiencies through any one of the following routes: a force-free, general-relativistic magnetohydrodynamic (GRMHD) or kinetic treatment of the low-field regime in which the Blandford–Znajek mechanism is inoperative because the field lies below the pair-production threshold of order $10^4$ G that sustains the magnetospheric charge (the regime in which Dadhich et al. (2018) predicted super-efficiency in magnetohydrodynamic flows); or a demonstration that the ultra-strong-field suppression mechanism does or does not operate in a plasma-filled magnetosphere. The chosen route need not model all of the listed effects, but must state which of them it includes and which it neglects.

3. Distinguishing diagnostics. Determine whether the predicted efficiency differences between Kerr black holes and Kerr superspinars (including the electron-versus-proton energy partition of the escaping fragments) translate into concrete observable diagnostics — power output, spectra, jet properties — by which a superspinar could be distinguished from a black hole in a realistic astrophysical setting.

The existence of ultra-strong fields $B \sim O(M^{-1})$ in nature and the microphysical value of the superspinar boundary radius $R_s$ are to be treated as input parameters, with conclusions required to state their robustness across plausible ranges, not as sub-problems to be solved.

References

1. R. Penrose, 'Gravitational collapse: The role of general relativity', Rivista del Nuovo Cimento 1, 252 (1969); reprinted as 'Golden Oldie' in General Relativity and Gravitation 34, 1141 (2002), DOI:10.1023/A:1016578408204, https://doi.org/10.1023/A:1016578408204
2. F. J. Ernst, 'Black holes in a magnetic universe', Journal of Mathematical Physics 17, 54 (1976), DOI:10.1063/1.522781, https://doi.org/10.1063/1.522781
3. R. M. Wald, 'Black hole in a uniform magnetic field', Physical Review D 10, 1680 (1974), DOI:10.1103/PhysRevD.10.1680, https://doi.org/10.1103/PhysRevD.10.1680
4. R. D. Blandford, R. L. Znajek, 'Electromagnetic extraction of energy from Kerr black holes', Monthly Notices of the Royal Astronomical Society 179, 433 (1977), DOI:10.1093/mnras/179.3.433, https://doi.org/10.1093/mnras/179.3.433
5. S. M. Wagh, S. V. Dhurandhar, N. Dadhich, 'Revival of the Penrose process for astrophysical applications', The Astrophysical Journal 290, 12 (1985), DOI:10.1086/162952, https://doi.org/10.1086/162952
6. N. Dadhich, 'Magnetic Penrose Process and Blanford-Zanejk mechanism: A clarification' (2012), arXiv:1210.1041, https://arxiv.org/abs/1210.1041
7. N. Dadhich, A. Tursunov, B. Ahmedov, Z. Stuchlík, 'The distinguishing signature of magnetic Penrose process', Monthly Notices of the Royal Astronomical Society: Letters 478, L89 (2018), DOI:10.1093/mnrasl/sly073, arXiv:1804.09679, https://arxiv.org/abs/1804.09679
8. A. Tursunov, N. Dadhich, 'Fifty years of energy extraction from rotating black hole: revisiting magnetic Penrose process', Universe 5(5), 125 (2019), DOI:10.3390/universe5050125, arXiv:1905.05321, https://arxiv.org/abs/1905.05321
9. J.-P. Lasota, E. Gourgoulhon, M. Abramowicz, A. Tchekhovskoy, R. Narayan, 'Extracting black-hole rotational energy: The generalized Penrose process', Physical Review D 89, 024041 (2014), DOI:10.1103/PhysRevD.89.024041, arXiv:1310.7499, https://arxiv.org/abs/1310.7499
10. Z. Stuchlík, M. Kološ, A. Tursunov, 'Penrose Process: Its Variants and Astrophysical Applications', Universe 7(11), 416 (2021), DOI:10.3390/universe7110416, https://doi.org/10.3390/universe7110416
11. C. Chakraborty, P. Patil, G. Akash, 'Magnetic Penrose process in the magnetized Kerr spacetime', Physical Review D 109, 064062 (2024), DOI:10.1103/PhysRevD.109.064062, arXiv:2401.13347, https://arxiv.org/abs/2401.13347
12. M. Kološ, A. Tursunov, Z. Stuchlík, 'Radiative Penrose process: Energy Gain by a Single Radiating Charged Particle in the Ergosphere of Rotating Black Hole', Physical Review D 103, 024021 (2021), DOI:10.1103/PhysRevD.103.024021, arXiv:2010.09481, https://arxiv.org/abs/2010.09481
13. L. Comisso, F. A. Asenjo, 'Magnetic Reconnection as a Mechanism for Energy Extraction from Rotating Black Holes', Physical Review D 103, 023014 (2021), DOI:10.1103/PhysRevD.103.023014, arXiv:2012.00879, https://arxiv.org/abs/2012.00879
14. S.-J. Zhang, 'Energy extraction via magnetic reconnection in magnetized black holes', Journal of Cosmology and Astroparticle Physics 07 (2024) 042, DOI:10.1088/1475-7516/2024/07/042, arXiv:2405.16941, https://arxiv.org/abs/2405.16941
15. S.-J. Zhang, 'Penrose process in magnetized non-Kerr rotating spacetime with anomalous quadrupole moment', Journal of Cosmology and Astroparticle Physics 12 (2025) 004, DOI:10.1088/1475-7516/2025/12/004, arXiv:2507.08401, https://arxiv.org/abs/2507.08401
16. K. Wang, X.-X. Zeng, 'Extracting Energy from Magnetized Rotating Black Holes in Horndeski Gravity via the Magnetic Penrose Process' (2026), arXiv:2603.29319, https://arxiv.org/abs/2603.29319
17. X.-X. Zeng, K. Wang, 'Repetitive Penrose process in accelerating Kerr black holes', Physics Letters B (2026), DOI:10.1016/j.physletb.2026.140727, arXiv:2601.01414, https://arxiv.org/abs/2601.01414
18. M. Mirkhaydarov, T. Xamidov, P. Sheoran, S. Shaymatov, H. Nandan, 'Non-monotonic enhancement of the Magnetic Penrose Process in Kerr-Bertotti-Robinson spacetime and its implication for electron acceleration', Journal of Cosmology and Astroparticle Physics 08 (2026) 035, DOI:10.1088/1475-7516/2026/08/035, arXiv:2601.09919, https://arxiv.org/abs/2601.09919
19. D. P. Viththani, T. Bhanja, V. Patel, P. S. Joshi, 'Magnetic Penrose process and Kerr black hole mimickers', Physical Review D 110, 123035 (2024), DOI:10.1103/PhysRevD.110.123035, arXiv:2407.19738, https://arxiv.org/abs/2407.19738
20. U. Fatima, G. Abbas, 'Penrose process in rotating black holes with quantum corrections: implications for energy extraction and irreducible mass', European Physical Journal C (2026), DOI:10.1140/epjc/s10052-026-15382-z, arXiv:2508.01683, https://arxiv.org/abs/2508.01683
21. M. Oh, M.-G. Park, 'Accelerated protons produced by magnetic Penrose process in Sgr A*', Physical Review D 110, 023015 (2024), DOI:10.1103/PhysRevD.110.023015, arXiv:2406.04764, https://arxiv.org/abs/2406.04764
22. J. S. Santos, V. Cardoso, J. Natário, 'Floating orbits and energy extraction from magnetized Kerr black holes', Physical Review D 110, 124054 (2024), DOI:10.1103/PhysRevD.110.124054, arXiv:2409.17225, https://arxiv.org/abs/2409.17225
23. E. G. Gimon, P. Hořava, 'Astrophysical violations of the Kerr bound as a possible signature of string theory', Physics Letters B 672, 299 (2009), DOI:10.1016/j.physletb.2009.01.026, arXiv:0706.2873, https://arxiv.org/abs/0706.2873
24. K.-i. Nakao, P. S. Joshi, J.-Q. Guo, P. Kocherlakota, H. Tagoshi, T. Harada, M. Patil, A. Królak, 'On the stability of a superspinar', Physics Letters B 780, 410 (2018), DOI:10.1016/j.physletb.2018.03.014, arXiv:1707.07242, https://arxiv.org/abs/1707.07242
25. R. Roy, P. Kocherlakota, P. S. Joshi, 'Mode stability of a near-extremal Kerr superspinar' (2019), arXiv:1911.06169, https://arxiv.org/abs/1911.06169
26. D. Charbulák, Z. Stuchlík, 'Light escape cones in the locally nonrotating reference frames of the Kerr-de Sitter superspinars and related superspinar shadows', Physical Review D 110, 124050 (2024), DOI:10.1103/PhysRevD.110.124050, arXiv:2410.17659, https://arxiv.org/abs/2410.17659
27. N. Uchikata, T. Narikawa, 'Prospects for estimating parameters from gravitational waves of superspinar binaries', Physical Review D 104, 024059 (2021), DOI:10.1103/PhysRevD.104.024059, arXiv:2104.12968, https://arxiv.org/abs/2104.12968
28. G. A. Piovano, A. Maselli, P. Pani, 'Model independent tests of the Kerr bound with extreme mass ratio inspirals', Physics Letters B 811, 135860 (2020), DOI:10.1016/j.physletb.2020.135860, arXiv:2003.08448, https://arxiv.org/abs/2003.08448
29. P. Pradhan, 'Distinguishing signature of Kerr-MOG black hole and superspinar via Lense-Thirring precession', European Physical Journal C (2024), DOI:10.1140/epjc/s10052-024-13210-w, arXiv:2408.14274, https://arxiv.org/abs/2408.14274
30. V. Patel, 'Energy extraction-driven instability and horizon formation in Kerr-Newman naked singularities and their limiting cases' (2026), arXiv:2603.10727, https://arxiv.org/abs/2603.10727
31. The Event Horizon Telescope Collaboration, 'First M87 Event Horizon Telescope Results. VIII. Magnetic Field Structure near The Event Horizon', The Astrophysical Journal Letters 910, L13 (2021), DOI:10.3847/2041-8213/abe4de, https://doi.org/10.3847/2041-8213/abe4de