Inverse Reconstruction of Causal Nonlinear Electrodynamics: Functional Families, Spectral Constraints, and Single-Horizon Black Holes
Abstract
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 𝒞X, 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≤1/2, 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 𝒞X 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.
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BibTeX
@misc{guzman2026inverse,
title = {{Inverse Reconstruction of Causal Nonlinear Electrodynamics: Functional Families, Spectral Constraints, and Single-Horizon Black Holes}},
author = {Ariel Guzmán and Mohsen Fathi and J. R. Villanueva},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.16016},
eprint = {2609.16016},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.16016},
}
RIS
TY - UNPB
TI - Inverse Reconstruction of Causal Nonlinear Electrodynamics: Functional Families, Spectral Constraints, and Single-Horizon Black Holes
AU - Ariel Guzmán
AU - Mohsen Fathi
AU - J. R. Villanueva
PY - 2026
DA - 2026/09/16
PB - arXiv
DO - 10.48550/arxiv.2609.16016
UR - https://arxiv.org/abs/2609.16016
AB - 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 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≤1/2, 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 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.
ER -