AI 中文总结
研究通过塞伯格 - 维滕映射对四元场非对易修正产生的变形施瓦西黑洞热力学性质，推导修正视界半径评估相关热力学量，研究蒸发过程，发现热容量有三个阶段，黑洞有有限寿命且引入基本长度尺度。
AI 中文摘要
我们研究了通过塞伯格 - 维滕映射对四元场进行新的非对易修正而产生的变形施瓦西黑洞的修正热力学性质。通过推导修正的事件视界半径，我们评估了相应的热力学量，包括霍金温度、熵、热容量、亥姆霍兹自由能和压力。我们还研究了此非对易框架内黑洞的蒸发过程。热容量行为揭示了一个丰富的热力学结构，由三个不同阶段组成：两个具有负热容量的不稳定阶段，分别对应大黑洞和小黑洞，中间由一个具有正热容量的稳定阶段隔开。我们的分析还表明，由于非对易性对黑洞质量的有效贡献，非对易几何中的施瓦西黑洞具有超过其经典对应物的有限寿命。非对易修正自然地引入了一个基本长度尺度\(\Theta = 1.6\times10^{-35}m\)，其量级为普朗克长度。
英文摘要
We investigate the modified thermodynamic properties of a deformed Schwarzschild black hole arising from new noncommutative corrections to the tetrad fields obtained through the Seiberg-Witten map. By deriving the corrected event horizon radius, we evaluate the corresponding thermodynamic quantities, including the Hawking temperature, entropy, heat capacity, Helmholtz free energy, and pressure. We also examine the evaporation process of the black hole within this noncommutative framework. The behavior of the heat capacity reveals a rich thermodynamic structure consisting of three distinct phases: two unstable phases with negative heat capacity, corresponding to a large black hole and a small black hole, separated by an intermediate stable phase with positive heat capacity. Our analysis also shows that the Schwarzschild black hole in noncommutative geometry possesses a finite lifetime that exceeds that of its classical counterpart, owing to the effective contribution of noncommutativity to the black hole mass. The noncommutative correction naturally introduces a fundamental length scale, Θ=1,6.10^-35 m, which is of the order of the Planck length.
Comments19 pages, 6 figures
