Gray-body factor and absorption of the Dirac field in ESTGB gravity

The gray-body factor and the absorption cross section of the 4D ESTGB gravity with a mode of nonlinear electrodynamics for the massless Dirac field are studied in this paper. The magnetic charge value varies between $-2^{(\frac{5}{3})}/3$ and $0$ as well as the ADM mass is set to $1$, which corresponds to a non-extreme black hole. The gray-body factor is obtained using the semi-analytic WKB method after solving the massless Dirac equation. When the absolute value of magnetic charge is increasing, the gray-body factor $\gamma(\omega)$ is decreasing. In addition, the partial absorption cross section and the total absorption cross section are calculated by using the partial wave method. We find that the maximum value of partial absorption cross section decreases as $\kappa$ increases. And the existence of magnetic charge causes the diminishing of the total absorption cross section. Finally, we find that the absorption cross section of the Dirac field is more sensitive to electric charge than magnetic charge by comparing the absorption cross section of the Reissner-Nordstr$\rm\ddot{o}$m and ESTGB-NLED black holes.