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It is known that the Meissner‐like effect is seen in a magnetosphere without an electric current in black hole space–time: no non‐monopole component of magnetic flux penetrates the event horizon if the black hole is extreme. In this paper, in order to see how an electric current affects the Meissner‐like effect, we study a force‐free electromagnetic system in a static and spherically symmetric extreme black hole space–time. By assuming that the rotational angular velocity of the magnetic field is very small, we construct a perturbative solution for the Grad–Shafranov equation, which is the basic equation to determine a stationary, axisymmetric electromagnetic field with a force‐free electric current. Our perturbation analysis reveals that, if an electric current exists, higher multipole components may be superposed upon the monopole component on the event horizon, even if the black hole is extreme.

Perturbative analysis of a stationary magnetosphere in an extreme black hole space–time: on the Meissner‐like effect of an extreme black hole