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 ( generalizations of the Maxwellian electromagnetism ) . We firstly solve Einstein field equations minimally coupled to an arbitrary ( current-free ) nonlinear Lagrangian of electrodynamics ( NLED ) in the slow rotation regime a \ll M ( black hole ’ s mass ) , up to first order in a / M . We then make use of the robust and self-contained Born-Infeld Lagrangian in order to compare and contrast the physical properties of such NLED spacetime with its Maxwellian counterpart ( a slowly rotating Kerr-Newman spacetime ) , especially focusing on the astrophysics of both neutrino flavor oscillations ( \nu _ { e } \rightarrow \nu _ { \mu } , \nu _ { \tau } ) and spin-flip ( \nu _ { l } \rightarrow \nu _ { r } , “ l ” stands for “ left ” and “ r ” stands for “ right ” , change of neutrino handedness ) mass level-crossings , the equivalent to gyroscopic precessions . Such analysis proves that in the spacetime of a slowly rotating nonlinear charged black hole ( RNCBH ) , intrinsically associated with the assumption the electromagnetism is nonlinear , the neutrino dynamics in core-collapse supernovae could be significantly changed . In such astrophysical environment a positive enhancement ( reduction of the electron fraction Y _ { e } < 0.5 ) of the r-process may take place . Consequently , it might result in hyperluminous supernova explosions due to enlargement , in atomic number and amount , of the decaying nuclides . Finally , we envisage some physical scenarios that may lead to short-lived charged black holes with high charge-to-mass ratios ( associated with unstable highly magnetized neutron stars ) and ways to possibly disentangle theories of the electromagnetism from other black holes observables ( by means of light polarization measurements ) .