We investigate the Blandford–Znajek process for an accelerating Kerr black hole described by the neutral rotating C-metric. In contrast with the usual asymptotically flat problem, the stationary magnetosphere lies between a black-hole horizon and an acceleration horizon. We derive the stationary, axisymmetric force-free stream equation in closed form and show that the overall conformal factor of the spacetime drops out of the electromagnetic problem. Requiring regularity at both future horizons determines the leading split-monopole solution: the magnetic field lines rotate at the mean rate of the two horizons, while the current is driven by their relative rotation. Consequently, the acceleration horizon suppresses the total extracted power. At the same time, the angular distortion associated with acceleration distributes the luminosity unequally between the two hemispheres, producing intrinsically asymmetric jets even when their unsigned magnetic fluxes are equal. The leading calculation is perturbative only in the black-hole rotation and retains the full allowed acceleration dependence. At the next rotational order, the flux equation separates into a weighted angular eigenvalue problem and independent radial boundary-value equations. This reduction establishes uniqueness of the regular correction, recovers the known Kerr sector when the acceleration is removed, and explains why a finite elementary angular ansatz is unavailable in the accelerated geometry. The fixed-acceleration slow-rotation expansion is not uniform when the horizon separation becomes comparable to the square of the spin; that near-coalescence regime requires a separate double-scaled solution.
- Open Access
- Article
The Blandford–Znajek Process for an Accelerating Kerr Black Hole
- Pakhlavon Jamolov 1,
- Sharofiddin Urinbaev 2,
- Gumisbek Allambergenov 2,
- Ozodbek Abdurakhmonov 2,*
Author Information
Received: 02 Sep 2026 | Revised: 26 Sep 2026 | Accepted: 28 Sep 2026 | Published: 30 Sep 2026
Abstract
Keywords
Blandford–Znajek process | accelerating black holes | rotating C-metric | force-free electrodynamics | relativistic jets | horizon regularity
References
- 1.
Blandford, R.D.; Znajek, R.L. Electromagnetic Extraction of Energy from Kerr Black Holes. Mon. Not. R. Astron. Soc. 1977, 179, 433–456. https://doi.org/10.1093/mnras/179.3.433.
- 2.
Znajek, R.L. Black Hole Electrodynamics and the Carter Tetrad. Mon. Not. R. Astron. Soc. 1977, 179, 457–472. https://doi.org/10.1093/mnras/179.3.457.
- 3.
Macdonald, D.A.; Thorne, K.S. Black‑Hole Electrodynamics: An Absolute‑Space/Universal‑Time Formulation*. Mon. Not. R. Astron. Soc. 1982, 198, 345–382. https://doi.org/10.1093/mnras/198.2.345.
- 4.
Komissarov, S.S. Electrodynamics of Black Hole Magnetospheres. Mon. Not. R. Astron. Soc. 2004, 350, 427–448. https://doi.org/10.1111/j.1365‑2966.2004.07598.x.
- 5.
McKinney, J.C.; Gammie, C.F. A Measurement of the Electromagnetic Luminosity of a Kerr Black Hole. Astrophys. J. 2004, 611, 977–995. https://doi.org/10.1086/422244.
- 6.
Tchekhovskoy, A.; Narayan, R.; McKinney, J.C. Black Hole Spin and the Radio Loud/Quiet Dichotomy of Active Galactic Nuclei. Astrophys. J. 2010, 711, 50–63. https://doi.org/10.1088/0004‑637x/711/1/50.
- 7.
Tchekhovskoy, A.; Narayan, R.; McKinney, J.C. Efficient Generation of Jets from Magnetically Arrested Accretion on a Rapidly Spinning Black Hole. Mon. Not. R. Astron. Soc. Lett. 2011, 418, L79–L83. https://doi.org/10.1111/j.1745‑3933.2011.01147.x.
- 8.
Meringolo, C.; Camilloni, F.; Rezzolla, L. Electromagnetic Energy Extraction from Kerr Black Holes: Ab Initio Calculations. Astrophys. J. Lett. 2025, 992, L8. https://doi.org/10.3847/2041‑8213/ae06a6.
- 9.
Gralla, S.E.; Jacobson, T. Spacetime Approach to Force‑Free Magnetospheres. Mon. Not. R. Astron. Soc. 2014, 445, 2500–2534. https://doi.org/10.1093/mnras/stu1690.
- 10.
Pan, Z.; Yu, C. Analytic Properties of Force‑Free Jets in the Kerr Spacetime—I. Astrophys. J. 2015, 812, 57. https://doi.org/10.1088/0004‑637x/812/1/57.
- 11.
Armas, J.; Cai, Y.; Compère, G.; et al. Consistent Blandford–Znajek Expansion. J. Cosmol. Astropart. Phys. 2020, 2020, 009. https://doi.org/10.1088/1475‑7516/2020/04/009.
- 12.
Camilloni, F.; Dias, O.J.C.; Grignani, G.; et al. Blandford‑Znajek Monopole Expansion Revisited: Novel Non‑Analytic Contributions to the Power Emission. J. Cosmol. Astropart. Phys. 2022, 2022, 032. https://doi.org/10.1088/1475‑7516/2022/07/032.
- 13.
Pei, G.; Nampalliwar, S.; Bambi, C.; et al. Blandford–Znajek Mechanism in Black Holes in Alternative Theories of Gravity. Eur. Phys. J. C 2016, 76, 534. https://doi.org/10.1140/epjc/s10052‑016‑4387‑z.
- 14.
Konoplya, R.A.; Kunz, J.; Zhidenko, A. Blandford‑Znajek Mechanism in the General Stationary Axially‑Symmetric Black‑Hole Spacetime. J. Cosmol. Astropart. Phys. 2021, 12, 002. https://doi.org/10.1088/1475‑7516/2021/12/002.
- 15.
Camilloni, F.; Harmark, T.; Orselli, M.; et al. Blandford‑Znajek Jets in MOdified Gravity. J. Cosmol. Astropart. Phys. 2024, 2024, 047. https://doi.org/10.1088/1475‑7516/2024/01/047.
- 16.
Camilloni, F.; Rezzolla, L. Universality of the Blandford‑Znajek Emission in Stationary and Axisymmetric Spacetimes. Phys. Rev. D 2026, 114, 023014. https://doi.org/10.1103/8b1s‑5mmm.
- 17.
Wang, X.; Ritz, A. Kerr‑AdS Black Holes and Force‑Free Magnetospheres. Phys. Rev. D 2014, 89, 106011. https://doi.org/10.1103/physrevd.89.106011.
- 18.
Hong, K.; Teo, E. A New Form of the Rotating C‑Metric. Class. Quantum Gravity 2005, 22, 109–117. https://doi.org/10.1088/0264‑9381/22/1/007.
- 19.
Griffiths, J.B.; Podolský, J. A New Look at the Plebański–Demiański Family of Solutions. Int. J. Mod. Phys. D 2006, 15, 335–369. https://doi.org/10.1142/s0218271806007742.
- 20.
Wang, K.; Zeng, X.X. Energy Extraction from the Accelerating Kerr Black Hole via Magnetic Reconnection in the Plunging Region and Circular Orbit Region. J. Cosmol. Astropart. Phys. 2025, 2025, 026. https://doi.org/10.1088/1475‑7516/2025/11/026.
- 21.
Luo, S. Thermodynamic Law and Holography Dual of Accelerating and Rotating Black Hole in Nariai Limit. Gen. Relativ. Gravit. 2025, 57, 137. https://doi.org/10.1007/s10714‑025‑03472‑4.
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