A class of nonstationary spacetimes is obtained by means of a conformal transformation of the Schwarzschild metric, where the conformal factor a(t) is an arbitrary function of the time coordinate only. We investigate several situations including some where the final state is a central object with constant mass. The metric is such that there is an initial big-bang type singularity and the final state depends on the chosen conformal factor. The Misner-Sharp mass is computed and a localized central object may be identified. The trapping horizons, geodesic and causal structure of the resulting spacetimes are investigated in detail. When a(t) asymptotes to a constant in a short enough time scale, the spacetime presents an event horizon and its analytical extension reveals black-hole or white-hole regions. On the other hand, when a(t) is unbounded from above as in cosmological models, the spacetime presents no event horizons and may present null singularities in the future. The energy-momentum content and other properties of the respective spacetimes are also investigated.

We study a class of charged cosmological black holes defined by the Shah-Vaidya solution, which is similar to the McVittie solution but for a central object of nonzero electric charge. We show that the Shah-Vaidya metric is a solution of Einstein's equations with a cuscuton and a Maxwell fields as sources, as well as a mass parameter. We then analyze the possible causal structures of the solution under some few physically reasonable assumptions, and determine the regions in the parameter space corresponding to well behaved charged cosmological black holes and those corresponding to naked singularities. The asymptotic behavior of the Hubble factor H(t) is also determinant to the causal properties of the spacetime and a theorem explaining its effect is stated. Examples of causal diagrams covering all the possibles types of spacetimes allowed by our initial assumptions are drawn and discussed.

Dirac fermions and electromagnetic fields are considered as the source of gravitation in the framework of standard Friedmann-Lemaître-Robertson-Walker (FLRW) cosmology. It is shown that all solutions for the scale-factor a(t) are non-singular, provided the cosmological constant Λ is set to be less than the positive inverse of a quantum scale.

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