Grey-Body Factors for Scalar and Dirac Fields in the Euler-Heisenberg Electrodynamics

Abstract: We study grey-body factors of neutral scalar and Dirac fields in the background of charged black holes arising in the Einstein--Euler--Heisenberg (EEH) theory. The Euler--Heisenberg corrections, which represent nonlinear electrodynamical effects due to vacuum polarization, modify the effective potential barrier surrounding the black hole and thereby affect the transmission probabilities for Hawking quanta. Using the sixth-order WKB method, and verifying our results against the recently proposed correspondence between grey-body factors and quasinormal modes, we compute the frequency-dependent grey-body spectra for various values of the black hole charge and EEH coupling. We find that the nonlinear coupling systematically lowers the effective potential barrier, enhancing the transmission probability. This work represents the first step toward incorporating nonlinear QED effects into the study of Hawking evaporation, focusing here on neutral test fields.