  Huge electromagnetic fields are known to be present during the late stages of
the dynamics of supernovae. Thus, when dealing with electrodynamics in this
context, the possibility may arise to probe nonlinear theories. The Einstein
field equations minimally coupled to an arbitrary nonlinear Lagrangian of
electrodynamics are solved in the regime of slow rotation, i.e. $a << M$ (black
hole's mass), up to first order in $a/M$. We use Born-Infeld Lagrangian to
compare the obtained results with Maxwellian counterpart. We focus on the
astrophysics of neutrino flavor oscillations ($\nu_e\to\nu_{\mu, \tau}$) and
spin-flip ($\nu_L\to\nu_R$), as well as on the computation of that the electron
fraction $Y_e$, hence the r-processes, which may significantly differ with
respect to the standard electrodynamics.
