Impact of Non-linear Interactions and the Coupling Constant λ on the Hawking Radiation Spectrum

In this work, we explore how non-linear quantum interactions, characterized by a coupling constant λ, modify the Hawking radiation spectrum in the context of black hole thermodynamics. While standard models of Hawking radiation assume linear field interactions, we incorporate the effects of non-linear coupling to investigate potential deviations in the emitted radiation. By numerically simulating these effects, we highlight the role of λ in altering both the temperature of the black hole and the overall particle emission spectrum. We demonstrate that modifications in the radiation spectrum, such as changes in polarization or asymmetries, are sensitive to the magnitude of λ offering insights into how quantum gravitational corrections can influence black hole evaporation. This work provides a new avenue for understanding quantum field dynamics in curved spacetimes and suggests possible experimental approaches for verifying these effects in both astrophysical and laboratory-based analog systems.