受量子引力启发的GUP有效度量
A Quantum-Gravity-Motivated GUP Effective Metric
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中文总结 AI 辅助
本研究构建受量子引力启发的尺度依赖二次型GUP有效度量，关联RG参数与GUP参数，改进黑洞热力学等预测，为GUP的基础描述提供新方向。
中文摘要 AI 辅助
近期的评论已探讨了广义不确定性原理（GUP）有效度量的某些方面（Ong 2023）。本研究提出一种尺度依赖的二次型GUP有效度量，通过分析引力诱导的相移（COW实验）和爱因斯坦-玻尔光子箱思想实验构建。与Xiang等人（2018）提出的方法不同，该依赖动量的度量通过引入插值函数Δp(r)得到改进，该函数利用有效距离概念，准确捕捉Δp(r)在短程和长程区域的不同行为。所得有效度量与从重整化群（RG）理论推导的结构相同，但RG参数γ̂现在可与无量纲GUP参数β₀关联，从而将该度量与基于RG的方法区分开。对应的有效度量预测显示模型具有内部一致性，且在现象学上，其预测在某些极限下与某些量子黑洞模型一致。与启发式方法和其他已提出的GUP有效度量相比，该有效度量改进了黑洞热力学和阴影预测。此外，GUP与f(R)引力（D'Agostino等人2026）之间的关系可能为更基础的GUP描述提供未来可能的途径。
英文摘要
Recent critiques have addressed certain aspects of the generalized uncertainty principle (GUP) effective metric (Ong 2023). This study presents a scale-dependent quadratic GUP effective metric, constructed through analyses of the gravity-induced phase shift (COW experiment) and the Einstein-Bohr photon box Gedanken experiment. In contrast to the procedure outlined in (Xiang et al. 2018), the momentum-dependent metric is improved by introducing an interpolating function $Δp (r)$, which employs the effective distance concept to accurately capture the distinct behavior of $Δp (r)$ in both short and long distance regimes. The resulting effective metric exhibits the same structure as that derived from the Renormalization Group (RG) theory. However, the RG parameter $\hatγ$ can now be related to the dimensionless GUP parameter $β_0$, thereby distinguishing this metric from the RG-based approach. The corresponding effective metric prediction demonstrates internal consistency of the model, and phenomenologically the predictions are in agreement with some quantum black hole models in some limits. The effective metric improved black hole thermodynamics and shadow predictions compared to the heuristic approach and other proposed GUP effective metrics. Furthermore, the relationship between GUP and $f(R)$ gravity (D'Agostino et al. 2026) may provide a possible future route toward a more fundamental description of GUP.
