Greybody Factors, Thermal Fluctuations, and Field Perturbations of Black Holes in Cotton Gravity Coupled to Nonlinear Electrodynamics

This paper examines the greybody factor for a black hole in the cotton gravity regime with non linear electrodynamics. The Klein-Gordon equation is used to determine the radial equation for a massless scalar field. Thus, the Schrodinger wave equation makes use of the tortoise coordinate system. This helps us compute the effective potential and its graphical analysis of different values of mass, charge, cotton gravity parameter, cosmological constant, and electromagnetic charge scalar. The exact solutions corresponding to the radial equation are computed at the event and the cosmological horizon by applying different transformations. Using these two solutions in the intermediate region, we first calculate the greybody factor and then investigate its corresponding graph. The greybody factor peaks reduce with mass and γ increases, which is directly proportional to l, F, q, r as well Λ. This indicates that absorption probability decreases for higher values of mass and cotton gravity parameter and modification increases the life of black hole. We further incorporate higher–order thermal fluctuation corrections to the black hole entropy and analyze their impact on thermodynamic stability. The corrected entropy, free energies, and specific heat reveal the presence of stable and unstable phases, with the cosmological constant Λ enhancing thermal stability while the Cotton gravity parameter γ tends to suppress it. In addition, scalar and electromagnetic field perturbations are investigated through their effective potentials and greybody factors. The results show that increasing black hole mass reduces the transmission probability of both scalar and vector modes, whereas electric charge and cosmological effects enhance wave propagation. Notably, electromagnetic perturbations exhibit a stronger sensitivity to charge variations than scalar modes, indicating distinct observational signatures in the Hawking radiation spectrum.