标题： 使用EHT结果测试线性二次GUP修正的Kerr黑洞 显示英文标题

标题： Testing linear-quadratic GUP modified Kerr Black hole using EHT results

摘要： 线性二次广义不确定性原理（LQG）与量子引力的各种理论提出的最小可测量长度和最大可测量动量的预测是一致的。 量子引力效应通过修改其ADM质量被引入到黑洞（BH）中。 在本文中，我们探讨了GUP对LQG修正的\k BH（LQKBH）光学特性的影响。 我们分析了BH的视界结构，这揭示了一个临界自旋值为 $7M/8$。 自旋 $(a)$小于临界值的BH对于任何实数的GUP参数 $\a$值都是可能的。 然而，当自旋超过临界值时，会出现一个不允许BH存在的 $\a$值的禁止区域。 随着自旋的增加，这个禁止区域会扩大。 我们随后考察$\a$对倾斜角$17^o$和$90^o$下黑洞阴影的形状和大小的影响，从而更深入地了解自旋和GUP对阴影的统一效应。 阴影的大小在$\a=1.0M$处达到最小值，而当自旋小于临界值时，对于$\a$的精确值，阴影偏离圆形的程度最大。 对于$a\,>\, 7M/8$未观察到极值。 阴影的大小和偏离程度会因倾斜角的减小而受到不利影响。 最后，我们将理论预测与事件视界望远镜合作提供的超大质量黑洞$M87^*$和$SgrA^*$的观测结果进行对比，以提取自转$a$和GUP参数$\a$的限制。 我们探讨了角直径$\th_d$、轴比$D_x$和偏离\s 半径$\d$的偏差，以构建对$a$和$\a$的约束。 我们的工作使LQKBHs成为天体物理黑洞的合理候选者。 显示英文摘要

摘要： The linear-quadratic Generalized uncertainty principle (LQG) is consistent with predictions of a minimum measurable length and a maximum measurable momentum put forth by various theories of quantum gravity. The quantum gravity effect is incorporated into a black hole (BH) by modifying its ADM mass. In this article, we explore the impact of GUP on the optical properties of an LQG modified \k BH (LQKBH). We analyze the horizon structure of the BH, which reveals a critical spin value of $7M/8$. BHs with spin $(a)$ less than the critical value are possible for any real GUP parameter $\a$ value. However, as the spin increases beyond the critical value, a forbidden region in $\a$ values pops up that disallows the existence of BHs. This forbidden region widens as we increase the spin. We then examine the impact of $\a$ on the shape and size of the BH shadow for inclination angles $17^o$ and $90^o$, providing a deeper insight into the unified effect of spin and GUP on the shadow. The size of the shadow has a minimum at $\a=1.0M$, whereas, for the exact value of $\a$, the deviation of the shadow from circularity becomes maximum when the spin is less than the critical value. No extrema is observed for $a\,>\, 7M/8$. The shadow's size and deviation are adversely affected by a decrease in the inclination angle. Finally, we confront theoretical predictions with observational results for supermassive BHs $M87^*$ and $SgrA^*$ provided by the EHT collaboration to extract bounds on the spin $a$ and GUP parameter $\a$. We explore bounds on the angular diameter $\th_d$, axial ratio $D_x$, and the deviation from \s radius $\d$ for constructing constraints on $a$ and $\a$. Our work makes LQKBHs plausible candidates for astrophysical BHs.