  We study the conditions of a possible static equilibrium between spherically
symmetric, electrically charged or neutral black holes and ambient matter. The
following kinds of matter are considered: (1) neutral and charged matter with a
linear equation of state p_r = w\rho (for neutral matter the results of our
previous work are reproduced), (2) neutral and charged matter with p_r \sim
\rho^m, m > 1, and (3) the possible presence of a "vacuum fluid" (the
cosmological constant or, more generally, anything that satisfies the equality
T^0_0 = T^1_1 at least at the horizon). We find a number of new cases of such
an equilibrium, including those generalizing the well-known Majumdar-Papapetrou
conditions for charged dust. It turns out, in particular, that ultraextremal
black holes cannot be in equilibrium with any matter in the absence of a vacuum
fluid; meanwhile, matter with w > 0, if it is properly charged, can surround an
extremal charged black hole.
