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The classic black hole mechanics and thermodynamics are formulated forstationary black holes with event horizons. Alternative theories of gravity ofinterest for cosmology contain a built-in time-dependent cosmological"constant" and black holes are not stationary. Realistic black holes are anywaydynamical because they interact with astrophysical environments or, at a morefundamental level, because of backreaction by Hawking radiation. In thesesituations the teleological concept of event horizon fails and apparent ortrapping horizons are used instead. Even as toy models, black holes embedded incosmological "backgrounds" and other inhomogeneous universes constitute aninteresting class of solutions of various theories of gravity. We discuss theknown phenomenology of apparent and trapping horizons in these geometries,focusing on spherically symmetric inhomogeneous universes.

Embedding black holes and other inhomogeneities in the universe in various theories of gravity: a short review