论文标题
广义扩展不确定性原理黑洞：宏观和微观领域中的阴影和镜头
Generalized Extended Uncertainty Principle Black Holes: Shadow and lensing in the macro- and microscopic realms
论文作者
论文摘要
在最近的有关扩展不确定性原理（EUP）黑洞\ Cite {Mureika：2018GXL}的动机中，我们在这项研究中提出了它的扩展，称为广义扩展不确定性原理（GEUP）黑洞。特别是，我们研究了对天体物理和微黑色孔的GEUP影响。首先，我们得出了阴影半径的表达，以研究其行为，这是由位于黑洞附近和遥远的静态观察者所感知的。还发现了使用EHT数据的限制较大的基本长度比例$ L*$最高$2σ$级别的限制：for sgr。 a*，$ l* = 5.716 \ text {x} 10^{10} $ m，而对于m87*，$ l* = 3.264 \ text {x} 10^{13} $ m。在GEUP效果下，由于静态观察者，阴影半径的价值与Schwarzschild案例相同，并且仅当Black Hole $ m $的质量与$ l _*$（或$ L_ \ l_ \ l_ \ text {pl text {pl}} $）的数量级左右出现。此外，GEUP效应增加了天体物理黑洞的阴影半径，但微黑色孔的相反发生。我们还探索了对弱偏转角度的GEUP效应，作为替代分析。对于这两个领域，时间样粒子都为弱偏转角度均具有更高的值。与阴影类似，当$ l _*$和$ m $的值接近时，可以看到偏差。在天体物理场景中，强挠度角对较小质量的GEUP偏差具有更大的敏感性。但是，弱挠度角是微世界中更好的探测。
Motivated by the recent work about the Extended Uncertainty Principle (EUP) black holes \cite{Mureika:2018gxl}, we present in this study its extension called the Generalized Extended Uncertainty Principle (GEUP) black holes. In particular, we investigated the GEUP effects on astrophysical and micro-black holes. First, we derive the expression for the shadow radius to investigate its behavior as perceived by a static observer located near and far from the black hole. Constraints to the large fundamental length scale $L*$ up to $2σ$ level were also found using the EHT data: for Sgr. A*, $L* = 5.716\text{x}10^{10}$ m, while for M87*, $L* = 3.264\text{x}10^{13}$ m. Under the GEUP effect, the value of the shadow radius behaves the same way as the Schwarzschild case due to a static observer, and the effect only emerges if the mass of the black hole $M$ is around the order of magnitude of $L_*$ (or $l_\text{Pl}$). In addition, the GEUP effect increases the shadow radius for astrophysical black holes, but the reverse happens for micro-black holes. We also explored GEUP effects to the weak and strong deflection angles as an alternative analysis. For both realms, a time-like particle gives a higher value for the weak deflection angle. Similar to the shadow, the deviation is seen when the values of $L_*$ and $M$ are close. The strong deflection angle gives more sensitivity to GEUP deviation at smaller masses in the astrophysical scenario. However, the weak deflection angle is a better probe in the micro world.
