  In our previous work [N. G\"urlebeck, M. Scholtz, Phys. Rev. D 95 064010
(2017)], we have shown that electric and magnetic fields are expelled from the
horizons of extremal, stationary and axially symmetric uncharged black holes;
this is called the Meissner effect for black holes. Here, we generalize this
result in several directions. First, we allow that the black hole carries
charge, which requires a generalization of the definition of the Meissner
effect.
  Next, we introduce the notion of almost isolated horizons, which is weaker
than the usual notion of isolated horizons, since the geometry of the former is
not necessarily completely time-independent. Moreover, we allow the horizon to
be pierced by strings, thereby violating the usual assumption on the spherical
topology made in the definition of the weakly isolated horizon. Finally, we
spell out in detail all assumptions entering the proof and show that the
Meissner effect is an inherent property of black holes even in full non-linear
theory.
