Fermion's tunnelling with effects of quantum gravity

TL;DR

This paper investigates fermion tunnelling in Schwarzschild spacetime considering quantum gravity effects, deriving corrected Hawking temperature and showing quantum gravity slows evaporation, leading to black hole remnants.

Contribution

It introduces quantum gravity corrections to fermion tunnelling and Hawking radiation, revealing effects on black hole evaporation and the formation of remnants.

Findings

Quantum gravity correction depends on fermion energy and black hole mass.

Corrected Hawking temperature decreases the evaporation rate.

Black hole remnants with mass $ extgreater extgreater M_p/eta_0$ are predicted.

Abstract

In this paper, using Hamilton-Jacobi method, we address the tunnelling of fermions in a 4-dimensional Schwarzschild spacetime. Base 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 $\gtrsim M_p/\beta_0$, 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.