Greybody Factor and Hawking Temperature of ModMax‐AdS Black Holes Surrounded by Perfect Fluid Dark Matter

Abstract This study presents an analytical formulation of the greybody factor for a ModMax‐AdS black hole surrounded by perfect fluid dark matter, derived by solving the Klein–Gordon equation under appropriate boundary conditions. Through a matching technique between near‐horizon and far‐field solutions, the absorption probability, energy emission rate as well as the absorption cross‐section for massless scalar fields are examined. The influence of physical parameters such as black hole mass, charge, ModMax parameter, cosmological length scale, and dark matter on the effective potential and greybody factor is thoroughly analyzed. The authors' results show that the greybody factor is sensitive to these parameters, with increased black hole mass, charge, and cosmological length scale leading to distinct modulations in the effective potential and greybody factor, indicating enhanced or reduced wave interactions. Additionally, the study incorporates the implications of the generalized uncertainty principle and dark matter on bosonic tunneling, revealing modified temperature and stability properties of the black hole. These findings manifest significant insights into the quantum field dynamics around black holes in curved spacetimes and contribute to the understanding of black hole thermodynamics in the presence of nonlinear electrodynamics and exotic matter.