The expression of the impact parameter, in the analysis for classical and semiclassical scattering cross sections for black holes, is obtained with nonlinear electrodynamics (NLED) while the absorption section is studied with the sinc approximation in the eikonal limit considering NLED.As an illustration we calculate the classical and semiclassical scattering as well as the absorption sections for three black holes under NLED, the magnetic Bardeen and Bronnikov black holes and the regular Euler-Heisenberg black hole. All are compared with the sections of their linear electromagnetic counterpart, the Reissner-Nordström (RN) black hole. The comparison shows how NLED affects the sections as well as the variation with respect to the Reissner-Nordström sections, in some cases these variations are small.
We analyzed the frequency shifts of photons emitted from massive particles that move in stable geodesics around black holes with non-linear electrodynamics. The motion of the photon is modified by an effective metric when the Einstein gravity is coupled with non-linear electrodynamics. The kinematic shifts for photons are modified by the magnetic and electric factors that make the difference between the linear and non-linear electrodynamics. As an illustration, we present the frequency shifts of the photons for black holes with non-linear electrodynamics, two magnetic black holes, and two electric black holes, the Bardeen and Bronnikov black holes for the magnetic charge and the Born-Infeld and Dymnikova black holes for electric charge. These frequency shifts are compared with their linear electromagnetic counterpart.
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