Abstract

Spacetimes representing black holes or central objects embedded in cosmological backgrounds provide explicit examples of time-dependent (apparent) horizons for the study of Hawking radiation and black hole thermodynamics in fully dynamical situations, allow one to explore the spatial variation of the gravitational coupling in scalar-tensor gravity, and help clarifying the long-standing issue of cosmological expansion versus local dynamics 1. Further, alternative gravity may be needed to explain the current acceleration of the universe without dark energy and theories designed for this purpose contain a time-dependent effective cosmological constant so that their black holes are asymptotically Friedmann-Lemâitre-Robertson-Walker (FLRW). Finally, they help studying the accretion of dark energy by black holes. A handful of spherical metrics describing inhomogeneities in FLRW backgrounds are known in General Relativity (GR) and in alternative gravity, but most are not understood. Relevant questions are: are there spacetime singularities, and are they hidden by apparent horizons (AHs)? Where are these AHs, do they expand, and how? Does the black hole mass (if a black hole exists) change? What are the matter sources and the conformal diagrams?

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