Recently there has been a surge of interest in regularizing, a $ D \to 4 $ limit of, the Einstein-Gauss-Bonnet (EGB) gravity, and the resulting regularized $4D$ EGB gravity has nontrivial dynamics. The theory admits spherically symmetric black holes generalizing the Schwarzschild black holes. We consider the rotating black hole in regularized $4D$ EGB gravity and discuss their horizon properties and shadow cast. The effects of the GB coupling parameter on the shape and size of shadows are investigated in the context of recent M87* observations from the EHT. Interestingly, for a given spin parameter, the apparent size of the shadow decreases and gets more distorted due to the GB coupling parameter. We find that within the finite parameter space, e.g. for $a=0.1M$, $\alpha\leq 0.00394M^2$, and within the current observational uncertainties, the rotating black holes of the $4D$ EGB gravity are consistent with the inferred features of M87* black hole shadow.

中文翻译：

---

4D Einstein-Gauss-Bonnet引力中的旋转黑洞及其阴影

最近，人们对正则化的兴趣激增，爱因斯坦-高斯-博内 (EGB) 引力的 $D\to 4 $ 限制，由此产生的正则化 $4D$ EGB 引力具有非平凡的动力学。该理论承认球对称黑洞概括了史瓦西黑洞。我们考虑正则化的 $4D$ EGB 引力中的旋转黑洞，并讨论它们的视界特性和阴影投射。GB 耦合参数对阴影形状和大小的影响在 EHT 近期 M87* 观测的背景下进行了研究。有趣的是，对于给定的自旋参数，由于 GB 耦合参数，阴影的表观大小会减小并变得更加失真。我们发现在有限的参数空间内，例如对于 $a=0.1M$, $\alpha\leq 0.00394M^2$，以及在当前的观测不确定性内，