Non-Linear Electrodynamics in Blandford–Znajek Energy Extraction

Non-linear electrodynamics (NLED) is a generalization of Maxwell's electrodynamics for strong fields. It has significant implications for the study of black holes and cosmology and has been extensively studied in the literature, extending from quantum to cosmological contexts. In this work, two new ways to investigate these non-linear theories are investigated. First, the Blandford-Znajek mechanism is analyzed 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. It is 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 seem to become vertical quickly. Considering only separated solutions, it is found that no monopole solutions exist and this could have interesting astrophysical consequences (not considered here). Last but not least, it is attempted to confine the NLED parameters by inducing the amplification of primordial magnetic fields (“seeds”), thus admitting non-linear theories already during the early stages of the Universe. However, the latter approach proves to be useful for NLED research only in certain models. These (analytical) results emphasize that the behavior of non-linear electromagnetic phenomena strongly depends on the physical context and that only a power-law model seems to have any chance to compete with Maxwell.