We study the Hawking radiation from the five-dimensional charged static squashed Kaluza–Klein black hole by the tunneling of charged scalar particles and charged fermions. In contrast to the previous studies of Hawking radiation from squashed Kaluza–Klein black holes, we consider the phenomenological quantum gravity effects predicted by the generalized uncertainty principle with the minimal measurable length. We derive corrections of the Hawking temperature to general relativity, which are related to the energy of the emitted particle, the size of the compact extra dimension, the charge of the black hole and the existence of the minimal length in the squashed Kaluza–Klein geometry. We obtain some known Hawking temperatures in five and four-dimensional black hole spacetimes by taking limits in the modified temperature. We show that the generalized uncertainty principle may slow down the increase of the Hawking temperature due to the radiation, which may lead to the thermodynamic stable remnant of the order of the Planck mass after the evaporation of the squashed Kaluza–Klein black hole. We also find that the sparsity of the Hawking radiation modified by the generalized uncertainty principle may become infinite when the mass of the squashed Kaluza–Klein black hole approaches its remnant mass.

中文翻译：

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基于广义不确定性原理的来自压缩 Kaluza-Klein 黑洞的标量粒子和费米子的霍金辐射

我们通过带电标量粒子和带电费米子的隧穿研究了来自五维带电静态压缩 Kaluza-Klein 黑洞的霍金辐射。与之前对来自压缩的 Kaluza-Klein 黑洞的霍金辐射的研究相比，我们考虑了由具有最小可测量长度的广义不确定性原理预测的现象学量子引力效应。我们推导出霍金温度对广义相对论的修正，这与发射粒子的能量、致密额外维度的大小、黑洞的电荷以及压缩的 Kaluza–Klein 几何中最小长度的存在有关. 我们通过限制修改后的温度，在五维和四维黑洞时空中获得了一些已知的霍金温度。我们表明，广义不确定性原理可能会减缓由于辐射引起的霍金温度的升高，这可能导致被压扁的卡鲁扎-克莱因黑洞蒸发后普朗克质量级的热力学稳定残余。我们还发现，当被压扁的 Kaluza-Klein 黑洞的质量接近其残余质量时，经广义测不准原理修正的霍金辐射的稀疏性可能会变得无穷大。