The EHT observation revealed event horizon-scale images of the supermassive black holes Sgr A* and M87* and these results are consistent with the shadow of a Kerr black hole as predicted by general relativity. However, Kerr-like rotating black holes in modified gravity theories can not ruled out, as they provide a crucial testing ground for these theories through EHT observations. It motivates us to investigate the bumblebee theory, a vector-tensor extension of the Einstein-Maxwell theory that permits spontaneous symmetry breaking, resulting in the field acquiring a vacuum expectation value and introducing Lorentz violation. We present rotating black holes within this bumblebee gravity model, which includes an additional parameter ℓ alongside the mass M and spin parameter a — namely RBHBG. Unlike the Kerr black hole, an extremal RBHBG, for ℓ < 0, refers to a black hole with angular momentum a > M. We derive an analytical formula necessary for the shadow of our rotating black holes, then visualize them with varying parameters a and ℓ, and also estimate the black hole parameters using shadow observables viz. shadow radius R_s , distortion δ_s , shadow area A and oblateness D using two well-known techniques. We find that ℓ incrementally increases the shadow size and causes more significant deformation while decreasing the event horizon area. Remarkably, an increase in ℓ enlarges the shadow radius irrespective of spin or inclination angle θ ₀.

中文翻译：

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研究熊蜂引力中的旋转黑洞：来自 EHT 观测的见解


EHT 观测揭示了超大质量黑洞 Sgr A* 和 M87* 的事件视界尺度图像，这些结果与广义相对论预测的克尔黑洞阴影一致。然而，不能排除修正引力理论中类似克尔的旋转黑洞，因为它们通过 EHT 观测为这些理论提供了重要的试验场。它促使我们研究大黄蜂理论，这是爱因斯坦-麦克斯韦理论的向量-张量扩展，它允许自发对称性打破，导致场获得真空期望值并引入洛伦兹违例。我们在这个熊蜂引力模型中展示了旋转黑洞，其中包括一个附加参数 l 以及质量 M 和自旋参数 a，即 RBHBG。与克尔黑洞不同，极值 RBHBG 对于 l < 0 是指角动量为 % 3E M 的黑洞。我们推导出旋转黑洞阴影所需的解析公式，然后使用不同的参数 a 和 l 可视化它们，并使用阴影可观测物（即阴影半径 R_s、失真 δ_s、阴影面积 A 和扁骨度 D）使用两种众所周知的技术来估计黑洞参数。我们发现 l 逐渐增加阴影大小并导致更显着的变形，同时减小事件视界面积。值得注意的是，l 的增加会扩大阴影半径，而与自旋或倾斜角 θ₀ 无关。