Black hole electrodynamics is defined as the theory of electro dynamic processes that can occur outside the event horizon, accessible to observation by distant observers. At first glance, black hole electrodynamics is quite trivial. Indeed, the electromagnetic field of a stationary black hole (of a given mass M) is determined unambiguously by its electric charge Q and rotation parameter a. If the charged black hole does not rotate, its electromagnetic field reduces to the radial electric field of the charge Q and is static. Any multipoles higher than the monopole are absent.

A charged rotating black hole induces a magnetic field and distorts the geometry of space and generates higher-order electric and magnetic moments. However, these higher-order moments are determined unambiguously by the quantities M, a, and Q. These moments are not independent, as one would find in the case of ordinary bodies.

In astrophysics, the electric charge of a black hole cannot be high. The magnetic field must also be very weak: the dipole magnetic moment of a black hole is μ^∗ = Qa. There can be no other stationary electromagnetic field inherent to a black hole. In this sense, the electrodynamics of, say, radio pulsars possessing a gigantic ‘frozen-in’ magnetic field of about 10¹² G is definitely much richer than that of the intrinsic fields of black holes.

However, if a black hole is placed in an external electromagnetic field and if charged particles are present in its surroundings, the situation changes dramatically and complex electrodynamics does appear. It is this aspect that we mean when black hole electrodynamics is discussed.

The case which is important for astrophysical applications is that of external magnetic (not electric) fields and rarefied plasma in which a black hole is embedded. In this system a regular magnetic field arises, for example, as it gets cleansed of magnetic loops which fall into a black hole. A regular magnetic field can also be generated in an accretion disk by the dynamo action.

In order to study the interaction of a black hole with its surrounding fields, we use the field equations and ‘total absorption’ boundary conditions at the surface of the black hole. The latter boundary conditions reflect the fact that the event horizon of a black hole is a null surface (at least at its regular points). Because of this property, the black hole horizon plays the role of a one-way membrane. Technically, this type of boundary condition which implies that the black hole interior cannot affect processes outside the horizon is quite simple, but it makes black holes different from usual astrophysical objects, which are bodies with a (timelike) boundary. It helps a lot, especially concerning our intuition, to develop a formalism in which black holes are more similar to ordinary physical objects. We describe briefly such an approach known as the ‘membrane paradigm’ and some important results of black hole electrodynamics.