存在最大长度和最小可测动量时的黑洞热力学
Black hole thermodynamics in the presence of a maximal length and minimum measurable in momentum
AI总结：
本研究纳入最小可测动量和最大长度效应，分析史瓦西黑洞热力学性质与安鲁效应，发现黑洞温度有最小值、质量有最大值，推导了熵和热容并确定稳定区间，还发现修正安鲁温度依赖于$α$。
摘要：
在本工作中，我们纳入最小可测动量和最大长度的效应，研究了史瓦西黑洞的热力学性质与安鲁效应。根据这一情形，我们发现黑洞温度不能小于某个最小值$T_{\text{min}}$，且黑洞质量不能大于某个最大值$M_{\text{max}}$。基于这些发现，我们首先计算了修正后的霍金温度与质量的关系并分析其特征行为，随后推导了黑洞的熵和热容，发现当$\frac{M_{\text{max}}}{\text{√3}}<M<M_{\text{max}}$时黑洞是稳定的。最后，我们研究了修正的安鲁效应，发现修正的安鲁温度明确依赖于$α$。
英文摘要：
In this work, incorporating the effect of the minimum measurable in momentum and maximal length, we studied thermodynamics property of Schwarzschild black hole and the Unruh effect. {\color{red} According to this scenario, we see that the black hole temperature cannot be smaller than a certain minimum value of $ T_{\min} $. Moreover, we find that black hole mass cannot be larger than a maximum mass value of $M_{\max }$. Considering these findings first we compute the corrected Hawking temperature versus the mass and examine its characteristic behavior. Then, we derive the black hole's entropy and heat capacity. We find that the black hole is stable when $\frac{M_{\max }}{\sqrt{3}}<M<M_{\max }$. Finally, we examined the modified Unruh effect. We find that the modified Unruh temperature explicitly depends on $α$.
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