发表机构
University of Santo Tomas; Eastern Mediterranean University; Mapúa University（圣多马大学; 东地中海大学; 马普阿大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究针对扩展不确定原理黑洞，采用固定ADM方案修正史瓦西外部解，分析其能量条件、熵的不匹配问题及相关物理效应，表征现象学族的最小成员。
AI 中文摘要
我们研究了一种用于对史瓦西外部解进行扩展不确定原理（EUP）修正的现象学固定ADM方案。我们未将质量恒定视为EUP的结果，而是保持在空间无穷远处测得的电荷固定，以便我们能比较相同物理质量下的外部解。我们施加了EUP偏移的视界半径和霍金温度，并选择最慢的可容许逆幂代表。其爱因斯坦张量定义了一个有效各向异性张量，但我们并未从该定义中推断出独立的物质模型、量子态或微扰理论。对于正的EUP参数，有效能量密度在整个外部区域均为负，而横向零能条件和强能条件在一段扩展的径向区域内不成立。面积熵与通过约化关系dM=TdS得到的形式熵在领头阶不一致；我们将这种不匹配解释为热力学描述缺乏功项或基于作用量的熵定律的证据，而非明确的EUP熵修正。具有相同质量、视界和温度的显式单参数族表明，轨道、透镜效应和测试场程函偏移取决于所选代表。因此，我们的结果表征的是现象学族的最小成员，而非EUP的普适性后果。
英文摘要
We study a phenomenological fixed-ADM prescription for an extended-uncertainty-principle (EUP) correction to the Schwarzschild exterior. Rather than treat mass constancy as a consequence of the EUP, we hold the charge measured at spatial infinity fixed so that we can compare exteriors at the same physical mass. We impose the EUP-shifted horizon radius and Hawking temperature and select the slowest admissible inverse-power representative. Its Einstein tensor defines an effective anisotropic tensor, but we do not infer an independent matter model, quantum state, or perturbation theory from that definition. For a positive EUP parameter, the effective energy density is negative throughout the exterior, while the transverse null and strong energy conditions fail over an extended radial region. The area entropy and the formal entropy obtained from the reduced relation $\mathrm{d}M=T\,\mathrm{d}S$ disagree at leading order; we interpret this mismatch as evidence that the thermodynamic description lacks work terms or an action-based entropy law, not as a definite EUP entropy correction. An explicit one-parameter family with the same mass, horizon, and temperature shows that the orbit, lensing, and test-field eikonal shifts depend on the chosen representative. Our results therefore characterize the minimal member of a phenomenological family rather than universal consequences of the EUP.
Comments13 pages, 3 captioned figures, 1 table
