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Peer-reviewedCC BY 4.0The European Physical Journal C

Nonlinear electrodynamics and stability of spherically symmetric space-times in scalar-tensor gravity

  • Kirill A. Bronnikov1,2,3
  • Rustam Ibadov4
  • Feruza Y. Shaymanova4,5
  • Najibullokhon M. Shukurullokhon4
5 affiliations
  1. 1Rostest
  2. 2RUDN University
  3. 3National Research Nuclear University “MEPhI”
  4. 4Samarkand State University
  5. 5Karshi State University
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Abstract

We study linear perturbations of static, spherically symmetric solutions of scalar-tensor theories (STT) of gravity from the Bergmann-Wagoner-Nordtvedt class, sourced by nonlinear electrodynamics (NED). We obtain a general expression for the effective potential Veff V eff governing the perturbation dynamics for theories with arbitrary scalar-electromagnetic interaction of the form L(ψ , F) L ( ψ , F ) , where ψ ψ is a scalar field and F = Fμ ν Fμ ν F = F μ ν F μ ν the electromagnetic invariant. This consideration includes, in particular, arbitrary scalar self-interaction potentials and scalar fields that can be phantom in some regions of space-time (the so-called trapped ghosts). Only radial (monopole) perturbations are considered here as the most likely ones to cause an instability. It is shown, in particular, that if NED has a correct Maxwell weak field limit, the zero charge limit of Veff V eff does not contain any trace of NED, and the perturbation dynamics is the same as for vacuum STT solutions. The previously obtained stability results for STT-Maxwell solutions are shown to be extended without change to STT-NED solutions with equal electric and magnetic charges, implying F =0 F = 0 . As an example of a solution with Fnot ≡ 0 F ≢ 0 , we consider a system with a massless scalar and truncated Born-Infeld NED, both minimally coupled to gravity, in GR, and show that almost all results previously obtained for F=0 F = 0 are qualitatively preserved.

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Cite

BibTeXRIS
BibTeX
@article{bronnikov2026nonlinear,
  title = {{Nonlinear electrodynamics and stability of spherically symmetric space-times in scalar-tensor gravity}},
  author = {Kirill A. Bronnikov and Rustam Ibadov and Feruza Y. Shaymanova and Najibullokhon M. Shukurullokhon},
  journal = {The European Physical Journal C},
  year = {2026},
  month = oct,
  doi = {10.1140/epjc/s10052-026-16469-3},
  url = {https://link.springer.com/article/10.1140/epjc/s10052-026-16469-3},
  note = {CC BY 4.0},
}
RIS
TY  - JOUR
TI  - Nonlinear electrodynamics and stability of spherically symmetric space-times in scalar-tensor gravity
AU  - Kirill A. Bronnikov
AU  - Rustam Ibadov
AU  - Feruza Y. Shaymanova
AU  - Najibullokhon M. Shukurullokhon
PY  - 2026
DA  - 2026/10/20
JO  - The European Physical Journal C
DO  - 10.1140/epjc/s10052-026-16469-3
UR  - https://link.springer.com/article/10.1140/epjc/s10052-026-16469-3
AB  - We study linear perturbations of static, spherically symmetric solutions of scalar-tensor theories (STT) of gravity from the Bergmann-Wagoner-Nordtvedt class, sourced by nonlinear electrodynamics (NED). We obtain a general expression for the effective potential V_eff V eff governing the perturbation dynamics for theories with arbitrary scalar-electromagnetic interaction of the form L(ψ , F) L ( ψ , F ) , where ψ ψ is a scalar field and F = F_μ ν F^μ ν  F = F μ ν F μ ν the electromagnetic invariant. This consideration includes, in particular, arbitrary scalar self-interaction potentials and scalar fields that can be phantom in some regions of space-time (the so-called trapped ghosts). Only radial (monopole) perturbations are considered here as the most likely ones to cause an instability. It is shown, in particular, that if NED has a correct Maxwell weak field limit, the zero charge limit of V_eff V eff does not contain any trace of NED, and the perturbation dynamics is the same as for vacuum STT solutions. The previously obtained stability results for STT-Maxwell solutions are shown to be extended without change to STT-NED solutions with equal electric and magnetic charges, implying F =0 F = 0 . As an example of a solution with Fnot ≡ 0 F ≢ 0 , we consider a system with a massless scalar and truncated Born-Infeld NED, both minimally coupled to gravity, in GR, and show that almost all results previously obtained for F=0 F = 0 are qualitatively preserved.
SN  - 1434-6044
SN  - 1434-6052
ER  -