Non-linear fermion dynamics, Hawking radiation, and dark energy: Thermodynamic implications for black hole evolution and cosmology

Abstract

The dynamics of fermion fields in curved spacetimes have garnered increasing attention in the context of black hole thermodynamics, particularly with respect to the generation of Hawking radiation. The present work explores the thermodynamic consequences of non-linear fermion dynamics, focusing on the role of non-Hermitian terms in the fermion field's Lagrangian. These modifications, which capture the dissipative effects inherent in black hole dynamics, are found to significantly influence the effective potential governing fermion propagation near the event horizon. The implications for the Hawking radiation spectrum, black hole evaporation, and the corresponding changes in the thermodynamic properties of the black hole are discussed. The inclusion of non-Hermitian terms is shown to accelerate the evaporation rate and modify the Hawking temperature, which has profound consequences for the black hole's long-term behavior and the stability of the quantum field.