Fermions Tunnelling with Quantum Gravity Correction

Based on the generalized uncertainty principle (GUP), we investigate the correction of quantum gravity to Hawking radiation of black hole by utilizing the tunnelling method. The result tells us that the quantum gravity correction retards the evaporation of black hole. Using the corrected covariant Dirac equation in curved spacetime, we study the tunnelling process of fermions in Schwarzschild spacetime and obtain the corrected Hawking temperature. It turns out that the correction depends not only on the mass of black hole but also on the mass of emitted fermions. In our calculation, the quantum gravity correction slows down the increase of Hawking temperature during the radiation explicitly. This correction leads to the remnants of black hole and avoids the evaporation singularity.