  In this work I studied the production of particles (electron-positron pairs
and photons) in the presence of overcritic ($\gg 4.4\cdot 10^{13}
\text{gauss}$) slowly varying magnetic fields. The calculations are performed
in the framework of QED in the presence of external not quantized
electromagnetic fields by means of the adiabatic perturbation theory. Also,
since such strong magnetic fields may be present near astrophysical compact
objects where gamma-ray bursts (GRB) are thought to be generated, I tried to
reproduce theoretically some features of the GRB energy spectra such as the low
energy ($\lesssim 0.1 \text{MeV}$) behaviour. Also, having in mind this
astrophysical scenario, I took into account the effects of a weak and of a
strong gravitational field on the production probabilities previously
calculated in the flat Minkowski spacetime.
