AI 中文总结
研究标量张量引力理论中由非线性电动力学源起的静态球对称解的线性微扰，通过得到有效势的一般表达式来分析，表明若NED有正确弱场极限，零电荷极限下微扰动力学与真空解相同，且相关稳定性结果可扩展。
AI 中文摘要
我们研究了由非线性电动力学（NED）源起的伯格曼 - 瓦格纳 - 诺德特维特类标量张量引力理论（STT）的静态、球对称解的线性微扰。对于具有任意标量 - 电磁相互作用形式$L(\psi, F)$的理论，我们得到了控制微扰动力学的有效势$V_{\rm eff}$的一般表达式，其中$\psi$是标量场，$F = F_{\mu\nu} F^{\mu\nu}$是电磁不变量。这里仅考虑径向（单极）微扰，因为它最有可能导致不稳定性。特别表明，如果NED具有正确的麦克斯韦弱场极限，$V_{\rm eff}$的零电荷极限不包含NED的任何痕迹，微扰动力学与真空STT解相同。先前获得的STT - 麦克斯韦解的稳定性结果在不改变的情况下扩展到具有相等电荷和磁荷（即$F =0$）的STT - NED解。
英文摘要
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 $V_{\rm eff}$ governing the perturbation dynamics for theories with arbitrary scalar-electromagnetic interaction of the form $L(ψ, F)$, where $ψ$ is a scalar field and $F = F_{μν} F^{μν}$ 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 $V_{\rm eff}$ 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 $F =0$.
Comments13 pages, no figures
