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arXiv · 2608.23620

An exact dyonic black hole at the integrable locus of quadratic nonlinear electrodynamics

Faizuddin Ahmed·Ahmad Al-Badawi·Izzet Sakalli
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Abstract

We obtain an exact dyonic black-hole solution in quadratic nonlinear electrodynamics defined by $-F+aF^{2}+bG^{2}$ on the special locus $b=a/2$. At this locus, the radial dependence in the electric constitutive relation cancels and the magnetic charge decouples, allowing the field equations to be integrated exactly. Using the field strength as the independent variable, we construct the solution in parametric closed form, with the radial quadrature expressed through Gauss hypergeometric functions and the cosmological constant retained. The solution recovers dyonic Reissner--Nordstr\"om--(anti-)de Sitter in the Maxwell limit, the known magnetic solution for vanishing electric charge, and the Euler--Heisenberg electric branch for vanishing magnetic charge. Its perturbative expansion agrees with the known dyonic result at first order and extends it to all orders. We find a three-horizon window requiring both electric and magnetic charges, while the corresponding Smarr integral is also expressed in closed hypergeometric form. The energy density and pressures are obtained analytically, showing that the electric charge enlarges the region satisfying the dominant energy condition relative to the purely magnetic case. Three distinct central curvature behaviors are identified, including a tuned self-energy singularity. We further develop the extended thermodynamics, treating the nonlinear coupling and pressure as thermodynamic variables, and find that the critical ratio decreases below the Maxwell value $3/8$ and disappears above a threshold coupling. Finally, birefringent photon propagation produces a split shadow doublet with a splitting of about $0.5\%$, whereas the geometric light ring and scalar ringdown are nearly insensitive to the nonlinear coupling, indicating that the main observable imprint of the nonlinearity lies in polarization-dependent photon propagation.

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Faizuddin Ahmed, Ahmad Al-Badawi, Izzet Sakalli. 2026-08-22. An exact dyonic black hole at the integrable locus of quadratic nonlinear electrodynamics. https://arxiv.org/abs/2608.23620

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