Hyperbolic scaling of the small-exponent limit in magnetic nonlinear electrodynamics
Abstract
A magnetic spacetime can approach Schwarzschild while its electromagnetic characteristics remain singular in the same parameter limit. We study this separation in fractional-power nonlinear electrodynamics as the exponent tends to zero with asymptotic mass, magnetic charge and nonlinear coupling independently fixed. The extraordinary polarization admits a common physical time direction only outside a boundary that grows as the inverse fourth root of the exponent. On this radial scale, the lapse tends to unity but the constitutive angular response retains a nondegenerate barrier and finite scaled critical data. An exact representation of the exterior electromagnetic energy yields complete second-order corrections to the orbit and impact, separating mass and charge contributions and their distinct cancellations. Constraining the mass to equal the electromagnetic self-energy preserves the leading critical constants while changing the approach from fourth-root to square-root corrections. Returning rays remain inside the admissible exterior and define a limiting scattering function with a calculated logarithmic strong-deflection coefficient. In the weak regime, constitutive bending decays as the inverse fourth power of scaled impact, whereas finite mass supplies a slower inverse-impact tail. We determine their competition scale, its accessibility above the critical impact, and the accuracy of the two-term approximation. Independent energy, orbit and scattering calculations check the expansions and resolve their parameter-dependent convergence. The analysis shows how a nearly vacuum background can support a distinct exterior optical limit through the nonlinear constitutive response.
Related
- Static Magnetic Brane Solutions in Quartic Quasi-Topological Gravity with Power-Law Maxwell Nonlinear Electrodynamics
- Novel topological subclasses of a magnetic black hole in causal nonlinear electrodynamics
- Static electric and magnetic traversable wormholes in (2+1)-dimensional nonlinear electrodynamics
- Static electric and magnetic traversable wormholes in (2+1)-dimensional nonlinear electrodynamics
- Nonlinear Quantum Optics in Epsilon-Near-Zero Nanospheres: a Macroscopic Quantum Electrodynamics Approach
BibTeX
@misc{reboucas2026hyperbolic,
title = {{Hyperbolic scaling of the small-exponent limit in magnetic nonlinear electrodynamics}},
author = {Jonathan A. Rebouças and R. Martínez von Dossow and Edson Otoniel},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.42091},
eprint = {2610.42091},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.42091},
}
RIS
TY - UNPB
TI - Hyperbolic scaling of the small-exponent limit in magnetic nonlinear electrodynamics
AU - Jonathan A. Rebouças
AU - R. Martínez von Dossow
AU - Edson Otoniel
PY - 2026
DA - 2026/10/30
PB - arXiv
DO - 10.48550/arxiv.2610.42091
UR - https://arxiv.org/abs/2610.42091
AB - A magnetic spacetime can approach Schwarzschild while its electromagnetic characteristics remain singular in the same parameter limit. We study this separation in fractional-power nonlinear electrodynamics as the exponent tends to zero with asymptotic mass, magnetic charge and nonlinear coupling independently fixed. The extraordinary polarization admits a common physical time direction only outside a boundary that grows as the inverse fourth root of the exponent. On this radial scale, the lapse tends to unity but the constitutive angular response retains a nondegenerate barrier and finite scaled critical data. An exact representation of the exterior electromagnetic energy yields complete second-order corrections to the orbit and impact, separating mass and charge contributions and their distinct cancellations. Constraining the mass to equal the electromagnetic self-energy preserves the leading critical constants while changing the approach from fourth-root to square-root corrections. Returning rays remain inside the admissible exterior and define a limiting scattering function with a calculated logarithmic strong-deflection coefficient. In the weak regime, constitutive bending decays as the inverse fourth power of scaled impact, whereas finite mass supplies a slower inverse-impact tail. We determine their competition scale, its accessibility above the critical impact, and the accuracy of the two-term approximation. Independent energy, orbit and scattering calculations check the expansions and resolve their parameter-dependent convergence. The analysis shows how a nearly vacuum background can support a distinct exterior optical limit through the nonlinear constitutive response.
ER -