Researchers have calculated the greybody factors and Hawking radiation spectra for a specific class of black holes with a positive cosmological constant, known as Einstein-Euler-Heisenberg-de Sitter black holes. This study focuses on the emission of neutral scalar particles and massless Dirac fermions from these objects, considering the finite region between the black hole event horizon and the cosmological horizon as a two-sided scattering problem. Calculations were performed using direct numerical integrations for the transmission coefficients and a sixth-order WKB approximation to verify the results near the maximum of the potential barrier.

The results show that, across the studied black hole family, an increase in the Euler-Heisenberg coupling raises the dominant barriers for scalar and Dirac particles, shifting the semi-transmission frequencies to higher values. Conversely, while keeping the charge and nonlinear coupling fixed, an increase in the cosmological constant contracts the static region and decreases the dominant greybody factor thresholds. These findings are crucial for understanding how the intrinsic properties of black holes and the cosmological environment influence radiation emission.

A key aspect of the study is the dependence of Hawking radiation luminosity on the temperature prescription used. Prescriptions based on the event horizon temperature predict an increase in emission as the nonlinear correction grows, whereas effective temperatures of the static region result in much lower emission rates and can even reverse the trend. This underscores that the interpretation of black hole evaporation is not unique and requires an explicit specification of the temperature convention to avoid ambiguities in understanding these astrophysical and theoretical phenomena.