In this paper, we have employed the second-order Lorentz invariance violation (LIV) to carefully investigate the effect of quantum gravity on the Hawking radiation of the Dirac particle via tunneling from the Kerr black hole. Firstly, it turns out that the Hawking temperature is not only related to the angular momentum and mass of the black hole, but related to the energy and mass of the emitted particle. In particular, we find that the effective temperature is bigger and bigger with the increase of the energy ω, the angular momentum j and the LIV parameter l _p , but is smaller and smaller with the increase of the black hole mass M. Also, it further shows that, although quantum gravity speeds up the black-hole evaporation, it will not evaporate completely, instead a remaining mass, temperature and entropy are left. Finally, through a careful count of the number of the microstates taken away by the black-hole radiation, the initial and remaining number of microstates for the Schwarzschild black hole are presented with the inclusion of the LIV-induced quantum gravity effects.

在本文中，我们采用了二阶洛伦兹不变性违背（LIV）方法，通过从Kerr黑洞中隧穿来仔细研究量子引力对Dirac粒子的Hawking辐射的影响。首先，事实证明霍金温度不仅与黑洞的角动量和质量有关，而且与所发射粒子的能量和质量有关。特别地，我们发现有效温度随着能量ω，角动量j和LIV参数l _p的增加而越来越大，但是随着黑洞质量M的增加而越来越小。 。而且，它进一步表明，尽管量子引力加速了黑洞的蒸发，但它不会完全蒸发，而是留下了剩余的质量，温度和熵。最后，通过仔细计算黑洞辐射带走的微状态数，可以得出包括Schwarzschild黑洞的微状态的初始数量和剩余数量，其中包括LIV引起的量子引力效应。