摘要：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 ≳ 𝑀𝑝/𝛽0, where 𝑀𝑝 is the Planck mass and 𝛽0 is a dimensionless
parameter accounting for quantum gravity effects. The evaporation singularity is then avoided.
