We consider rational nonlinear electrodynamics with the Lagrangian [Formula: see text] ([Formula: see text] is the Lorentz invariant), proposed in Ref. 63, coupled to General Relativity. The effective geometry induced by nonlinear electrodynamics corrections are found. We determine shadow’s size of regular non-rotating magnetic black holes and compare them with the shadow size of the super-massive M87[Formula: see text] black hole imaged by the Event Horizon Telescope collaboration. Assuming that the black hole mass has a pure electromagnetic nature, we obtain the black hole magnetic charge. The size of the shadow obtained is very close to the shadow size of non-regular neutral Schwarzschild black holes. As a result, we can interpret the super-massive M87[Formula: see text] black hole as a regular (without singularities) magnetized black hole.

中文翻译：

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有理非线性电动力学中M87∗黑洞的影子

我们用参考文献中提出的拉格朗日[公式：见文本]（[公式：见文本]是洛伦兹不变量）来考虑有理非线性电动力学。63，耦合到广义相对论。发现了由非线性电动力学校正引起的有效几何形状。我们确定了常规非旋转磁性黑洞的阴影大小，并将它们与事件视界望远镜合作拍摄的超大质量 M87[公式：见正文] 黑洞的阴影大小进行了比较。假设黑洞质量具有纯电磁性质，我们得到黑洞磁荷。得到的阴影大小非常接近非常规中性史瓦西黑洞的阴影大小。因此，我们可以将超大质量 M87[公式：见正文] 黑洞解释为一个规则的（无奇点）磁化黑洞。