Non-linear electrodynamics (NLED) is a generalization of Maxwell’s
electrodynamics for strong fields, where vacuum polarization in quantum
electrodynamics (QED) results in nonlinear interaction between the
electromagnetic fields (EMF). This interaction might lead to a new field of
nonlinear electrodynamics, which could have significant implications for the
study of black holes and cosmology and have been extensively studied in the
literature, extending from quantum to cosmological contexts. Recently, its
application to black holes, inflation and dark energy has caught on, being able
to provide an accelerated Universe and address some current theoretical
inconsistencies, such as the Big Bang singularity. In this work, we have
analyzed the Blandford-Znajeck mechanism in light of this promising theoretical
context, providing the general form of the extracted power up to second order
in the black hole spin parameter a. We have found that, depending on the NLED
model, the emitted power can be extremely increased or decreased, and that the
magnetic field lines around the black hole seems to become vertical quickly.
Considering only separated solutions, we have found that no monopole solutions
exist and this could have interesting astrophysical consequences. Finally, we
have tried to constrain the NLED parameters by forcing the amplification of
primordial magnetic fields, finding that this could be a good way to study NLED
only in some models. Last but not least, we attempted to confine the NLED
parameters by inducing the amplification of primordial magnetic fields, however
this approach proved to be effective for NLED research only in certain models.

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