Static electric and magnetic traversable wormholes in (2+1)-dimensional nonlinear electrodynamics
Abstract
Every traversable wormhole reported so far in static (2+1) gravity coupled to nonlinear electrodynamics has come from a power-Maxwell Lagrangian L propto |F|^k restricted to k=1/2, always forcing the cosmological constant to a fixed sign or zero. We show these restrictions are artefacts of that single choice, not physical requirements, and give a complete classification of static traversable wormholes in this theory. Of the three mutually exclusive electromagnetic configurations compatible with the symmetry, the radial electric branch admits no throat for any Lagrangian or Lambda. In each remaining branch, azimuthal electric and magnetic, the field equations admit exactly two regimes: either the redshift function is fixed, leaving the shape function b(r) completely free with Lambda absorbed without constraint; or the redshift is generic, in which case b(r) becomes fixed instead. We solve both regimes in closed form in both branches, and show that fixing the Lagrangian to any single power k forces Lambda nonzero and determines b(r) up to finitely many constants: this freedom requires the Lagrangian to be genuinely unrestricted. One azimuthal-electric family reproduces the static BTZ mass function, turning the vacuum black hole into a wormhole once sourced by the nonlinear field. Applied to the unique conformal power-Maxwell theory, k=3/4, previously known only as a radial-branch charged black hole, the same Lagrangian yields genuine wormholes in the azimuthal and magnetic branches, showing the electromagnetic configuration, not the Lagrangian, decides between a horizon and a throat; Born-Infeld electrodynamics admits no throat in any branch.
Related
- Physical properties of charged black holes from the nonlinear electrodynamics model based on electric potential regularization
- Black bounces to traversable wormholes from pure gravity in four and higher dimensions
- Traversable Casimir Wormholes with Gravitational Memory
- Higher-Dimensional Slowly Rotating Black Holes in Nonlinear Electrodynamics
- Global Integrated Null Energy Contribution : Classification of Traversable Wormholes
BibTeX
@misc{cataldo2026static,
title = {{Static electric and magnetic traversable wormholes in $(2+1)$-dimensional nonlinear electrodynamics}},
author = {Mauricio Cataldo},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2608.21283},
eprint = {2608.21283},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.21283},
}
RIS
TY - UNPB
TI - Static electric and magnetic traversable wormholes in (2+1)-dimensional nonlinear electrodynamics
AU - Mauricio Cataldo
PY - 2026
DA - 2026/10/15
PB - arXiv
DO - 10.48550/arxiv.2608.21283
UR - https://arxiv.org/abs/2608.21283
AB - Every traversable wormhole reported so far in static (2+1) gravity coupled to nonlinear electrodynamics has come from a power-Maxwell Lagrangian L propto |F|^k restricted to k=1/2, always forcing the cosmological constant to a fixed sign or zero. We show these restrictions are artefacts of that single choice, not physical requirements, and give a complete classification of static traversable wormholes in this theory. Of the three mutually exclusive electromagnetic configurations compatible with the symmetry, the radial electric branch admits no throat for any Lagrangian or Lambda. In each remaining branch, azimuthal electric and magnetic, the field equations admit exactly two regimes: either the redshift function is fixed, leaving the shape function b(r) completely free with Lambda absorbed without constraint; or the redshift is generic, in which case b(r) becomes fixed instead. We solve both regimes in closed form in both branches, and show that fixing the Lagrangian to any single power k forces Lambda nonzero and determines b(r) up to finitely many constants: this freedom requires the Lagrangian to be genuinely unrestricted. One azimuthal-electric family reproduces the static BTZ mass function, turning the vacuum black hole into a wormhole once sourced by the nonlinear field. Applied to the unique conformal power-Maxwell theory, k=3/4, previously known only as a radial-branch charged black hole, the same Lagrangian yields genuine wormholes in the azimuthal and magnetic branches, showing the electromagnetic configuration, not the Lagrangian, decides between a horizon and a throat; Born-Infeld electrodynamics admits no throat in any branch.
ER -