Based on string theory, loop quantum gravity, black hole physics, and other theories of quantum gravity, physicists have proposed generalized uncertainty principle (GUP) modifications. In this work, within the framework of GUP gravity theory, we successfully derive an exact solution to Einstein’s field equation, and discuss the possibility of using EHT to test GUP and how GUP changes the weak cosmic censorship conjecture for black holes. We analyze two different ways of constructing GUP rotating black holes (model I and model II). Model I takes into account the modification of mass by GUP, i.e., the change in mass by quantization of space, and the resulting GUP rotating black hole metric (18) is similar in form to the Kerr black hole metric. Model II takes into account the modification of the rotating black hole when GUP is an external field, where GUP acts like an electric charge, and the resulting GUP rotating black hole metric (19) is similar in form to the Kerr–Newman black hole metric. The difference between (18) and (19) in the spacetime linear structure provides a basis for us to examine the physical nature of GUP rotating black holes from observation. By analyzing the shadow shape of the GUP rotating black hole, we discover intriguing characteristics regarding the impact of first-order and second-order momentum correction coefficients on the black hole’s shadow shape. These findings will be instrumental in future GUP testing using EHT. Additionally, by incident test particle and scalar field with a rotating GUP black hole, the weak cosmic censorship conjecture is not violated in either extreme black holes or near-extreme black holes.

基于弦理论、圈量子引力、黑洞物理和其他量子引力理论，物理学家提出了广义不确定性原理（GUP）的修正。在这项工作中，我们在GUP引力理论的框架内，成功推导了爱因斯坦场方程的精确解，并讨论了利用EHT测试GUP的可能性以及GUP如何改变黑洞的弱宇宙审查猜想。我们分析了构建 GUP 旋转黑洞的两种不同方法（模型 I 和模型 II）。模型I考虑了GUP对质量的修改，即空间量子化引起的质量变化，得到的GUP旋转黑洞度量(18)在形式上与克尔黑洞度量相似。模型 II 考虑了当 GUP 为外场时旋转黑洞的修正，其中 GUP 的作用类似于电荷，由此产生的 GUP 旋转黑洞度量 (19) 与 Kerr-Newman 黑洞度量在形式上类似。式(18)和式(19)在时空线性结构上的差异为我们从观测中检验GUP旋转黑洞的物理性质提供了基础。通过分析GUP旋转黑洞的阴影形状，我们发现了关于一阶和二阶动量校正系数对黑洞阴影形状影响的有趣特征。这些发现将有助于未来使用 EHT 进行 GUP 测试。此外，通过旋转 GUP 黑洞的事件测试粒子和标量场，无论是极端黑洞还是近极端黑洞都没有违反弱宇宙审查猜想。