PreprintarXiv licencearXiv
An Electrodynamic Lifting of the Toda Monopoles in Curved 3+1 Spacetime
Abstract
Every solution of the hyperbolic Toda equation determines a classical Abelian monopole on a (2+1)-dimensional Einstein--Weyl space. We determine when its connection is also a source-free electromagnetic potential on a curved Lorentzian 3+1 spacetime with a spacelike Killing field. On the generic branch, Maxwell's equation classifies the admissible Killing-fibre scale and horizontal twist through one characteristic of the Toda field. A separated Liouville branch gives purely magnetic fields with considerably freer fibre geometry. The round spherical solution yields a monopole of unit charge with conserved flux on a contracting screen. The background metric here is neither assumed to be Einstein nor self-dual.
Related
BibTeX
@misc{liu2026electrodynamic,
title = {{An Electrodynamic Lifting of the Toda Monopoles in Curved 3+1 Spacetime}},
author = {Hanwen Liu},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.20272},
eprint = {2609.20272},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.20272},
}
RIS
TY - UNPB
TI - An Electrodynamic Lifting of the Toda Monopoles in Curved 3+1 Spacetime
AU - Hanwen Liu
PY - 2026
DA - 2026/09/01
PB - arXiv
DO - 10.48550/arxiv.2609.20272
UR - https://arxiv.org/abs/2609.20272
AB - Every solution of the hyperbolic Toda equation determines a classical Abelian monopole on a (2+1)-dimensional Einstein--Weyl space. We determine when its connection is also a source-free electromagnetic potential on a curved Lorentzian 3+1 spacetime with a spacelike Killing field. On the generic branch, Maxwell's equation classifies the admissible Killing-fibre scale and horizontal twist through one characteristic of the Toda field. A separated Liouville branch gives purely magnetic fields with considerably freer fibre geometry. The round spherical solution yields a monopole of unit charge with conserved flux on a contracting screen. The background metric here is neither assumed to be Einstein nor self-dual.
ER -