Fermion's Tunnelling with Effects of Quantum Gravity

In this paper, using Hamilton-Jacobi method, we address the tunnelling of fermions in a 4-dimensional Schwarzschild spacetime. Based on the generalized uncertainty principle, we introduce the influence of quantum gravity. After solving the equation of motion of the spin-1/2 field, we derive the corrected Hawking temperature. It turns out that the correction depends not only on the black hole's mass but also on the mass (energy) of emitted fermions. It is of interest that, in our calculation, the quantum gravity correction decelerates the temperature increase during the radiation explicitly. This observation then naturally leads to the remnants in black hole evaporation. Our calculation shows that the residue mass is greater than or similar to M-p/beta(0), where M-p is the Planck mass and beta(0) is a dimensionless parameter accounting for quantum gravity effects. The evaporation singularity is then avoided.