Charged black holes in expanding Einstein–de Sitter universes
Inspired by a previous work by McClure and Dyer (2006) (Class. Quantum Grav. 23 1971), we analyze some solutions of the Einstein–Maxwell equations that 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 we then 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 SD metric requires a global electric current, besides a central (spherically symmetric) electric charge. With the aim of comparing to the charged McVittie metric, new charged solutions of Vd and SD types 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 SD 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 SD 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.