标题： 非线性电动力学黑洞及其在检验引力修改理论中的作用 显示英文标题

标题： Nonlinear electrodynamic black holes and their role in testing modified theories of gravity

摘要： 黑洞（BHs）的性质及其与经典广义相对论（GR）的潜在偏差仍然是现代天体物理学中的核心问题。非线性电动力学（NED）提供了一种有前景的机制，用于构建避免奇点的同时保留关键天体物理特性的常规黑洞。在本工作中，我们分析了受NED启发的黑洞，并利用事件视界望远镜（EHT）观测数据进行贝叶斯参数估计，得出了磁参数的约束。我们得到了M87*的$q = 0.63 ^{+0.68}_{-0.44} \times 10^9 M_{\odot}$和Sgr A*的$q = 0.33 ^{+0.36}_{-0.23} \times 10^6 M_{\odot}$，这些参数影响了它们的视界结构。与施瓦茨希尔德解的比较突显了几何结构和视界性质的偏差，强调了NED的影响。我们还研究了观测特征，包括黑洞阴影和引力透镜效应。使用$R_{\text{sh}} = r_{\text{ph}} \sqrt{1/f(r_{\text{ph}})}$，我们在均匀和非均匀等离子体条件下探索了阴影特征，揭示了由于NED效应导致的与GR预测的偏差。通过分析光子球位移和透镜模式，我们识别了区分这些黑洞与经典黑洞的可观测特征。我们的结果表明，NED引起的修改可能在强场区域留下可检测的痕迹，为测试替代引力模型开辟了途径。未来的任务，如激光干涉空间天线（LISA）和新一代X射线天文台，以及EHT的持续观测和激光干涉引力波天文台与Virgo（LIGO--Virgo）的引力波探测，对于完善这些模型的约束将是至关重要的。 显示英文摘要

摘要： The nature of black holes (BHs) and their potential deviations from classical General Relativity (GR) remain central questions in modern astrophysics. Nonlinear electrodynamics (NED) offers a promising mechanism to construct regular BHs that avoid singularities while retaining key astrophysical features. In this work, we analyze NED-inspired BHs and derive constraints on the magnetic parameter using Bayesian parameter estimation from Event Horizon Telescope (EHT) observations. We obtain $q = 0.63 ^{+0.68}_{-0.44} \times 10^9 M_{\odot}$ for M87* and $q = 0.33 ^{+0.36}_{-0.23} \times 10^6 M_{\odot}$ for Sgr A*, affecting their horizon structure. A comparison with the Schwarzschild solution highlights deviations in geometry and horizon properties, emphasizing the impact of NED. We also examine observational signatures, including BH shadows and gravitational lensing. Using $R_{\text{sh}} = r_{\text{ph}} \sqrt{1/f(r_{\text{ph}})}$, we explore shadow features under uniform and non-uniform plasma conditions, revealing deviations from GR predictions due to NED effects. By analyzing photon sphere shifts and lensing patterns, we identify observable features that distinguish these BHs from classical ones. Our results suggest that NED-induced modifications may leave detectable imprints in strong-field regimes, opening pathways to test alternative gravity models. Future missions such as the Laser Interferometer Space Antenna (LISA) and next-generation X-ray observatories, along with ongoing observations from the EHT and gravitational wave detections by the Laser Interferometer Gravitational-Wave Observatory and Virgo (LIGO--Virgo), will be essential for refining constraints on such models.