发表机构
Institute of Physics and Astronomy, Faculty of Sciences, Universidad de Valparaíso; Center for Research in Space Sciences and Theoretical Physics (CICEF), Universidad Central de Chile（瓦尔帕莱索大学理学院物理与天文学研究所; 智利中央大学空间科学与理论物理研究中心）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文通过逆问题方法重构因果非线性电动力学，获得无限维函数族，证明Born-Infeld为唯一自对偶成员，并给出单视界黑洞解与光学度量闭式形式。
AI 中文摘要
我们将非线性电动力学表述为一个本构逆问题：在选取拉格朗日量之前，先施加可积性、麦克斯韦极限和因果传播条件。在双不变量的仿射可分约化下，我们获得了一个无限维因果类，其函数自由度由一个有界对数指标编码。该类一般非自对偶；Born-Infeld 是其唯一的自对偶成员，并且它包含超越已知幂律线的闭式双折射理论。在磁轴上，完全单调性产生一个正谱表示。有限单极子自能等价于阶为 $-1/4$ 的谱矩。全局磁因果性迫使谱支撑在原点处累积，而有限自能则排除原点处的原子；这些条件共同排除了有限原子测度。对于广义伽马谱，全局磁因果性和有限自能对每个形状参数都选择了精确窗口 $1/4<γ\leq 1/2$。我们进一步确定了这些磁定律何时允许因果双不变量完备化，并给出了完整类中非幂成员的显式谱实现。将重构的物质耦合到爱因斯坦引力会产生精确几何和一个单调性判据，该判据允许至多一个正视界。最后，我们以闭式形式获得了完整类的两个光学度量，并证明它们具有相交的因果锥，从而在所述正则性假设下确立了对称双曲性。
英文摘要
Nonlinear electrodynamics (NLED) admits many causal theories, so causality alone does not provide a unique selection principle. We formulate an inverse construction in which constitutive integrability, the Maxwell weak-field limit, and causal propagation are imposed before either a Lagrangian or a spacetime geometry is chosen. An affine-separable reduction of the two-invariant Plebański class yields an infinite-dimensional causal family $\mathcal{C}_X$, characterized by a bounded logarithmic index; Born-Infeld is its unique self-dual member, while generic members are birefringent. On the magnetic axis, complete monotonicity gives a positive spectral representation. Finite monopole self-energy is equivalent to the existence of the spectral moment of order $-1/4$, whereas global magnetic causality restricts the support. Generalized-gamma spectra are simultaneously causal and finite-energy precisely for $1/4<γ\le1/2$, independently of the shape parameter, and a separate criterion determines when the magnetic law admits a causal two-invariant completion. After coupling to Einstein gravity, a positive magnetic response and characteristic factor, finite self-energy, and nonnegative residual mass imply a strictly increasing metric function, excluding more than one positive horizon; positive residual mass guarantees a unique horizon. The two optical metrics of $\mathcal{C}_X$ remain Lorentzian with overlapping timelike cones, establishing symmetric hyperbolicity of the electromagnetic subsystem. Thus inverse matter selection connects local causal consistency to global black-hole structure without prescribing the geometry.
Comments24 pages, 1 table. Revised and streamlined presentation, with clearer statements of novelty, scope, and relation to previous work. Discussion and typesetting have also been improved. Main results are unchanged
