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We study rotating black holes in general relativity coupled to nonlinear electrodynamics (NED), focusing on the axisymmetric solution of Annals Phys. 434 (2021) 168619 with deformation parameter g. On the spherical seed, weak-field lensing via the Gauss-Bonnet method and the shadow radius yield a spin-insensitive bound by enforcing a conservative ∼10% tolerance on the Sgr A* ring size, namely g/M≲1.26. In the eikonal regime we derive analytic quasinormal-mode shifts (even in g) and obtain an independent ceiling consistent with the shadow constraint Eur. Phys. J. C 79 (2019) 629. For the rotating geometry, we provide closed-form ZAMO scalars, chart horizons and ergoregion, and analyze equatorial geodesics (photon orbits and ISCO). We then formulate in the ZAMO frame the Comisso-Asenjo reconnection channel Phys. Rev. D 103 (2021) 023014, identify the negative-energy window, and integrate the extracted power over the allowed radii; from the tolerated fractional departure from the Kerr power we define a spin-dependent extraction bound g δ (a|σ 0 ,ξ). Taken together, the QNM/shadow ceiling and the extraction bound appreciably narrow the admissible region for g/M in the (a/M, g/M), so even within our deliberately simplified, single-layer equatorial setup, the two complementary probes already provide informative constraints on NED deformations, testable with present data and upcoming horizon-scale/ringdown campaigns.
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Figliolia et al. (2026) studied this question.
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