  We construct explicit examples of globally regular static, spherically
symmetric solutions in general relativity with scalar and electromagnetic
fields describing traversable wormholes with flat and AdS asymptotics and
regular black holes, in particular, black universes. (A black universe is a
regular black hole with an expanding, asymptotically isotropic space-time
beyond the horizon.) The existence of such objects requires invoking scalars
with negative kinetic energy ("phantoms", or "ghosts"), which are not observed
under usual physical conditions. To account for that, the so-called "trapped
ghosts" were previously introduced, i.e., scalars whose kinetic energy is only
negative in a restricted strong-field region of space-time and positive outside
it. This approach leads to certain problems, including instability (as is
illustrated here by derivation of an effective potential for spherical
pertubations of such systems). In this paper, we use for model construction
what we call "invisible ghosts", i.e., phantom scalar fields sufficiently
rapidly decaying in the weak-field region. The resulting configurations contain
different numbers of Killing horizons, from zero to four.
