Non-linear Electrodynamics in Blandford-Znajeck Energy Extraction

TL;DR

This paper explores the effects of non-linear electrodynamics on black hole energy extraction via the Blandford-Znajeck mechanism, revealing model-dependent power variations and implications for astrophysics and early Universe magnetic fields.

Contribution

It introduces two new methods to analyze NLED in black hole physics, providing the general form of energy extraction power and examining the existence of monopole solutions.

Findings

Power output varies significantly with NLED models.

Magnetic field lines tend to become vertical near black holes.

Monopole solutions are absent in separated solutions.

Abstract

Non-linear electrodynamics (NLED) is a generalization of Maxwell's electrodynamics for strong fields. It 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 report two new ways to investigate these non-linear theories. First, 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 (not considered here). Last but not least, we 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 proved to be useful for NLED research only in certain models. Our (analytical) results emphasize that the existence and behavior of non-linear electromagnetic phenomena strongly depend on the physical context and that only a power-low model seems to have any chance to compete with Maxwell.