  Inspired in a previous work by McClure and Dyer (Classical Quantum Gravity
23, 1971 (2006)), we analyze some solutions of the Einstein-Maxwell equations
which were originally written to describe charged black holes in cosmological
backgrounds. A detailed analysis of the electromagnetic sources for a
sufficiently general metric is performed, and then we focus on deriving the
electromagnetic four-current as well as the conserved electric charge of each
metric. The charged McVittie solution is revisited and a brief study of its
causal structure is performed, showing that it may represent a charged black
hole in an expanding universe, with the black hole horizon being formed at
infinite late times. Charged versions of solutions originally put forward by
Vaidya (Vd) and Sultana and Dyer (SD) are also analyzed. It is shown that the
charged Sultana-Dyer metric requires a global electric current, besides a
central (pointlike) electric charge. With the aim of comparing to the charged
McVittie metric, new charged solutions of Vd and SD type are considered. In
these cases, the original mass and charge parameters are replaced by particular
functions of the cosmological time. In the new generalized charged Vaidya
metric the black hole horizon never forms, whereas in the new generalized
Sultana-Dyer case both the Cauchy and the black hole horizons develop at
infinite late times. A charged version of the Thakurta metric is also studied
here. It is also a new solution. As in the charged Sultana-Dyer case, the
natural source of the electromagnetic field is a central electric charge with
an additional global electric current. The global structure is briefly studied
and it is verified that the corresponding spacetime may represent a charged
black hole in a cosmological background. All the solutions present initial
singularities as found in the McVittie metric.
