Note on the Corrected Hawking Temperature of a Parametric Deformed Black Hole with Influence of Quantum Gravity

In this paper, using the Hamilton-Jacobi method, we discuss the tunnelling of fermions when the dual influence of quantum gravity and the deformation of a parameterized black hole are taken into account. With the influence of the generalized uncertainty principle, there exists an offset around the standard Hawking temperature. We investigate a parametric deformed black hole and find that the corrected temperature is lower than the standard one, so there exists a remnant of the black hole, and the correction is not only determined by the mass and the energy of the emitted fermion but also determined by the mass of the black hole and the deformation parameter. Under the dual influence of quantum gravity and deformation, the correction effect of quantum gravity is the main influencing factor, while the correction effect of the deformation parameter is secondary. For both the massive and massless cases, the quantum gravity correction factor is only determined by the energy of the emitted fermion, while the deformation correction factor is only determined by the mass of the black hole.