Black hole magnetospheres in the Born–Infeld theory

Abstract

We study the force-free electrodynamics on rotating black holes in the Born-Infeld (BI) effective theory. The stream equation describing a steady and axisymmetric magnetosphere is derived. From its near-horizon behavior, we obtain the modified Znajek regularity condition, with which we find that the horizon resistivity in the BI theory is generally not a constant. As expected, the outer boundary condition far away from the hole remains unchanged. In terms of the conditions at both boundaries, we derive the perturbative solution of split monopole in the slow rotation limit. It is interesting to realise that the correction to the solution relies not only on the parameter in the BI theory, but also on the radius (or the mass) of the hole. We also show that the quantum effects can undermine the energy extraction process of the magnetosphere in the non-linear theory and the extraction rate gets the maximum in the Maxwell theory.The force-free magnetosphere can be used to extract the rotational energy of a rotating black hole. As a kind of Penrose process, the energy is extracted through the rotation of the magnetosphere dragged by the black hole spacetime. This process has become a promising mechanism nowadays that can explain the formation of powerful jets observed in many high energy objects, like AGN, GRB and microquasars.It is known that the magnetic fields on neutron stars are very high, even exceeding the quantum electrodynamics (QED) critical value. In this case, the QED corrections should be included in the force-free magnetospheres and the Maxwell electrodynamics should be replaced by the non-linear theory. This has been discussed in magnetar magnetospheres (e.g., [2,3,4]), whose surface magnetic fields sometimes can be above 10 15 G.However, this is not the case for black hole magnetospheres. The astronomical black holes do not have their own magnetic fields. The magnetic fields on them come from accretion and are usually far weaker (e.g., 10 4 G for a black hole with mass M = 10 9 M ⊙ [5]) than the QED critical value. But, the study of the black hole magnetosphere in non-linear electrodynamics is useful for that of the QED corrected magnetosphere near a magnetar where gravity is important. The latter can be obtained in a weak field limit of the former despite a difference of the inner boundary condition.The study of black hole magnetospheres in non-linear electrodynamics is also of theoretical interest. The force-free magnetospheres on black holes are not well understood even in the Maxwell theory. We still do not know well the structure and geometry of the field lines in the force-free magnetosphere. The extension to the non-linear theory help find the analytical properties of black hole magnetospheres in a general sense.Moreover, non-linear electrodynamics include quantum corrections to the Maxwell theory. As is known, strong quantum effects also happen in black holes. Thermal particles are excited and radiated in the near-horizon regions of black holes. It is interesting to examine the force-free non-lin...

Magnetically charged black holes from non-linear electrodynamics and the Event Horizon Telescope

“…Black hole solutions in NLED models were studied in a wide number of papers. For instance, within BI NLED, an incomplete list of works studying BH solutions can be found in [127][128][129][130][131][132][133][134][135][136][137][138][139][140][141]. Similar studies within the context of Euler-Heisenberg non-linear electrodynamics can instead be found in [120,[142][143][144][145][146][147][148][149][150].…”

Magnetically charged black holes from non-linear electrodynamics and the Event Horizon Telescope

“…Black hole solutions in NLED models were studied in a wide number of papers. For instance, within BI NLED, an incomplete list of works studying BH solutions can be found in [127][128][129][130][131][132][133][134][135][136][137][138][139][140][141]. Similar studies within the context of Euler-Heisenberg non-linear electrodynamics can instead be found in [120,[142][143][144][145][146][147][148][149][150].…”