Coupled gravitoelectromagnetic response of a magnetically supported generalized Hayward black hole in nonlinear electrodynamics

Abstract

We construct the exterior coupled gravitational and electromagnetic response of a magnetically supported generalized Hayward black hole within a specified nonlinear electrodynamic completion. Starting from the linearized Einstein nonlinear electrodynamic equations, we make the magnetic parity pairing explicit, eliminate the nondynamical constraints, and fix a flux normalized two channel basis; the resulting real symmetric operator is the one used in all spectral and scattering calculations. Its asymptotic \(r^{-2}\) term fixes an effective Reissner–Nordström comparator through \(Q_\textrm{eff}^{2}/M^{2}=2\varepsilon \), leaving no adjustable charge in the comparison; the nonlinear electrodynamic horizon branch itself extends beyond the RN extremality bound for this same asymptotic charge. The effective charged operator captures the dominant weak core mixing, while the nonlinear electrodynamic information is isolated by quantities that vanish in the Einstein Maxwell limit: parity asymmetry, metric-optical characteristic splitting, and the residual after effective charged subtraction. At \(\chi =0.98\), the quadrupolar parity asymmetries are 1.12% and 2.56% for the primarily gravitational and electromagnetic branches, and the metric-optical critical scale differs by about 3%. The weak core residuals are consistent with cubic spectral corrections in the primarily electromagnetic branch and quartic corrections in the primarily gravitational branch and principal scattering observables. The large quadrupolar conversion is predominantly effective charged and is therefore used as a response benchmark rather than as a unique nonlinear electrodynamic signature.