Nonlinear electrodynamics and stability of spherically symmetric space-times in scalar-tensor gravity
Year: 2026
Type: article
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 $$V_\textrm{eff}$$ V eff governing the perturbation dynamics for theories with arbitrary scalar-electromagnetic interaction of the form $$L(\psi , F)$$ L ( ψ , F ) , where $$\psi $$ ψ is a scalar field and $$F = F_{\mu \nu }F^{\mu \nu }$$ 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 $$V_\textrm{eff}$$ 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 $$F\not \equiv 0$$ 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.
Source: The European Physical Journal C
Language: English
Subfield: Astronomy and Astrophysics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: diamond
Awards: G4552033650, G872658069
OpenAlex ID: W7168235585