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On the Motion of a Point Electric Charge in the Field of Wu-Yang Monopoles in Bertotti-Robinson Spacetimes

  • Tekin Dereli
  • Yorgo Senikoglu
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Abstract

We study the SU(2) Einstein-Yang-Mills system with non-minimal RF2-type couplings of Yang-Mills fields to curvature, formulated with exterior differential forms and a Lagrange-multiplier constraint for the Levi-Civita connection. We show that the conformally flat Bertotti-Robinson geometry AdS2× S2 carries the Wu-Yang magnetic pole as an exact solution for arbitrary non-minimal couplings; the couplings only renormalise the radius of the S2. The non-conformally-flat branch of solutions known for this system is recalled. The Hopf fibration S3/S2≅ S1 of the gauge group manifold projects the Wu-Yang field on a uniform Dirac-type magnetic field, and the motion of a point electric charge in it is solved in closed form: the charge moves on a cone and oscillates between the horizon and a maximal radius.

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Cite

BibTeXRIS
BibTeX
@misc{dereli2026motion,
  title = {{On the Motion of a Point Electric Charge in the Field of Wu-Yang Monopoles in Bertotti-Robinson Spacetimes}},
  author = {Tekin Dereli and Yorgo Senikoglu},
  howpublished = {arXiv},
  year = {2026},
  month = nov,
  doi = {10.48550/arxiv.2611.04816},
  eprint = {2611.04816},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2611.04816},
}
RIS
TY  - UNPB
TI  - On the Motion of a Point Electric Charge in the Field of Wu-Yang Monopoles in Bertotti-Robinson Spacetimes
AU  - Tekin Dereli
AU  - Yorgo Senikoglu
PY  - 2026
DA  - 2026/11/03
PB  - arXiv
DO  - 10.48550/arxiv.2611.04816
UR  - https://arxiv.org/abs/2611.04816
AB  - We study the SU(2) Einstein-Yang-Mills system with non-minimal RF^2-type couplings of Yang-Mills fields to curvature, formulated with exterior differential forms and a Lagrange-multiplier constraint for the Levi-Civita connection. We show that the conformally flat Bertotti-Robinson geometry AdS_2× S^2 carries the Wu-Yang magnetic pole as an exact solution for arbitrary non-minimal couplings; the couplings only renormalise the radius of the S^2. The non-conformally-flat branch of solutions known for this system is recalled. The Hopf fibration S^3/S^2≅ S^1 of the gauge group manifold projects the Wu-Yang field on a uniform Dirac-type magnetic field, and the motion of a point electric charge in it is solved in closed form: the charge moves on a cone and oscillates between the horizon and a maximal radius.
ER  -