标题： 时空曲率引起的不确定性原理：将大尺度全局效应与局域黑洞物理联系起来 显示英文标题

标题： Spacetime-curvature induced uncertainty principle: linking the large-structure global effects to the local black hole physics

摘要： 本文将广义不确定性原理的高级表述形式——称为渐近广义扩展不确定性原理（AGEUP）——与粒子论框架联系起来，以推导出AGEUP启发的黑洞度规。前者结合时空曲率效应来探索量子引力修正下的黑洞动力学，而后者则认为黑洞是弱相互作用引力子的玻色-爱因斯坦凝聚体。在特定情况下，AGEUP（宇宙常数为$\Lambda$）与粒子论框架的结合产生了一个具有缩放质量的黑洞度规，该质量取决于$\Lambda$和普朗克长度$l_{\rm Pl}$。 一些有趣的推论随之出现，例如质量$M$的最大限制，在此限制下$\Lambda$停止影响黑洞。另一个推论是，如果大尺度基本长度仅定义为宇宙视界，则EUP项调制因子$\alpha$的推导值。通过阴影和偏折角现象进行了额外分析，从而得出了量子引力调制参数$\beta$的约束条件。 讨论了事件视界望远镜（EHT）和甚长基线干涉测量（VLBI）的约束条件，作为验证黑洞阴影半径和偏折角中AGEUP相关偏差的途径，为天体物理尺度上的量子引力效应提供了潜在的观测证据。 研究结果表明，AGEUP可能为黑洞的量子引力性质提供线索，特别是在高能天体物理背景下。通过将局部黑洞物理与大尺度曲率效应联系起来，AGEUP为量子引力和宇宙学交叉领域的进一步研究铺平了道路，对观测天文学和时空的基本结构具有重要意义。 显示英文摘要

摘要： This paper links the advanced formulation of the Generalized Uncertainty Principle, termed the Asymptotic Generalized Extended Uncertainty Principle (AGEUP), to the corpuscular framework to derive the AGEUP-inspired black hole metric. The former incorporates spacetime curvature effects to explore black hole dynamics under quantum gravitational corrections, while the latter is a view that black holes are Bose-Einstein condensates of weakly interacting gravitons. In a particular case, the phenomenological union between the AGEUP with cosmological constant $\Lambda$ to the corpuscular framework enabled a black hole metric that has a scaled mass, which depends on $\Lambda$ and the Planck length $l_{\rm Pl}$. Interesting implications occur, such as the maximum limit for mass $M$ where $\Lambda$ ceases to influence the black hole. Another is the derived value of the modulation factor of the EUP term, $\alpha$, if the large-scale fundamental length is defined solely as the cosmological horizon. Additional analyses were done through the shadow and deflection angle phenomena, deriving constraints on the quantum gravity modulation parameter $\beta$. Constraints from the Event Horizon Telescope (EHT) and Very Long Baseline Interferometry (VLBI) are discussed as avenues for verifying AGEUP-related deviations in black hole shadow radius and deflection angles, offering potential observational evidence of quantum gravitational effects at astrophysical scales. The findings suggest that AGEUP could be instrumental in providing hints on the quantum gravity nature of black holes, particularly in high-energy astrophysical contexts. By linking local black hole physics with large-scale curvature effects, AGEUP paves the way for further research at the intersection of quantum gravity and cosmology, with implications for observational astrophysics and the fundamental structure of spacetime.