AI 中文总结
该研究探讨非对易动量依赖时空几何中的黑洞，通过引入量子修正的时空重整化方法，验证量子改进的雷斯纳-诺德斯特龙解与弱引力猜想的一致性，其红外行为可重现庞加莱代数的经典结果。
AI 中文摘要
我们研究动量依赖时空几何中的黑洞（BHs），并评估其量子雷斯纳-诺德斯特龙（RN）解与弱引力猜想（WGC）的一致性。通过非对易动量空间代数引入量子修正作为量子化过程，采用时空重整化方法作为动量空间与时空空间之间的映射。对于史瓦西情形，热力学分析表明，当蒸发停止（熵变为零）时存在一个热（非零温度）黑洞残余，满足黑洞热力学的第三定律互补形式。我们将该框架扩展至RN解并研究其极端极限。对于质量M远大于普朗克质量（M_P）的大质量黑洞，量子改进的RN几何在极端情形下表现出非零霍金温度，这与WGC一致，WGC规定极端态不应完全稳定或处于低温。所得的动量依赖度规和热力学性质在红外（IR）区域可重现庞加莱代数（经典模型）的结果。
英文摘要
We investigate black holes (BHs) in momentum-dependent spacetime geometry and assess its quantum Reissner-Nordström (RN) consistency with the weak gravity conjecture (WGC). Quantum corrections are introduced through the non-commutative momentum space algebra as the quantization process, and spacetime renormalization approach as a map between momentum and spacetime spaces. For the Schwarzschild case, thermodynamic analysis indicates the existence of a hot (non-zero temperature) BH remnant when evaporation stops (the entropy becomes zero), obeying a complementary third law for black hole thermodynamics. We extend this framework to the RN solution and examine its extremal limit. For large BHs with $M \gg M_P$ ($M_P$ for Planck mass), the quantum-improved RN geometry exhibits a non-zero Hawking temperature in the extremal case, consistent with the WGC, which stipulates that extremal states should not be exactly stable or cold. The resulting momentum-dependent metric and thermodynamic properties are shown to reproduce the results derived from the Poincaré algebra (classical model) in the infrared (IR) regime.
Comments13 pages, 5 figures
