## Magnetic fields around black holes

Do extremely rotating black holes power relativistic jets? A compelling answer may be beyond our reach yet for some time. For sure, magnetic fields play an important role in astrophysics. Near rotating compact objects, neutron stars and black holes, the field lines are wildly deformed by rapidly moving plasma and strong gravitational fields.

The electromagnetic field is governed by Maxwell's equations. These are the first-order differential equations for the electric and magnetic intensity vectors. When expressed in the equivalent, and perhaps more elegant tensorial formalism, the mutually coupled equations for the field intensities can be unified in terms of the electromagnetic field tensor, comprising both the electric and the magnetic field components in a single quantity. As is well known, the latter approach turns out to be particularly useful in the framework of the theory of relativity. Whichever of the two formulations is preferred, one has to tackle differential equations and, therefore, the appropriate initial and boundary conditions must be specified in order to determine the structure of the field completely.

Magnetic fields can extract rotational energy from the black hole back, and convert it to the outflowing Poynting flux and to kinetic energy of accelerated plasma flows. Such outflows are indeed observed, but the regions where they originate remain below resolution capabilities of present-day techniques. We discuss magnetized black holes, including the exact solutions within the framework of general relativity.

In our recent work we have proposed that the conditions in the ergosphere can lead to magnetic reconnection occurring in strong gravitational field of a rotating black hole. We also study the onset of chaotic motion in black hole magnetospheres, as well as the possibility of stable rotational motion in the off-equatorial lobes of magnetized compact stars and black holes, that is kind of Stoermer mechanism with gravitational effects taken into account.