AI 中文总结
本文在二次非线性电动力学的可积轨迹上构造出精确双荷黑洞解，其可恢复多种极限解，扩展了相关微扰结果，研究了其热力学性质与光子传播特性，发现非线性耦合对阴影分裂等偏振相关观测有显著影响。
AI 中文摘要
我们在由$-F+aF^{2}+bG^{2}$定义的二次非线性电动力学的特殊轨迹$b=a/2$上，获得了一个精确的双荷黑洞解。在该轨迹下，电本构关系中的径向依赖被抵消，磁荷解耦，使得场方程可被精确积分。我们以场强作为自变量，构造了参数化闭合形式的解，其中径向 quadrature（积分）通过高斯超几何函数表示，并保留了宇宙学常数。该解在麦克斯韦极限下可恢复双荷赖斯纳-诺德斯特龙-(反-)德西特黑洞，在电荷消失时可恢复已知的磁单极解，在磁荷消失时可恢复欧拉-海森堡电分支解。其微扰展开在一阶时与已知的双荷结果一致，并将其扩展至所有阶。我们发现存在一个需要同时具有电荷和磁荷的三视界窗口，而对应的斯马尔积分也以闭合超几何形式表示。能量密度和压力被解析得到，结果表明，与纯磁荷情况相比，电荷扩大了满足主导能量条件的区域。我们还识别出三种不同的中心曲率行为，包括调谐自能奇点。我们进一步发展了扩展热力学，将非线性耦合和压力作为热力学变量处理，发现临界比降至麦克斯韦值$3/8$以下，且在耦合超过阈值时消失。最后，双折射光子传播产生约$0.5\%$分裂的双阴影，而几何光环和标量振铃几乎对非线性耦合不敏感，这表明非线性的主要可观测印记在于依赖偏振的光子传播。
英文摘要
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--Nordström--(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.
