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Working in the semi-classical setting, we present an exactly solvable candidate model for astrophysical black holes, which can be embedded in a cosmological background and possess regular apparent horizons that form in finite observational time. We construct near-horizon quantities from the assumption of regularity of the renormalized expectation value of the energy-momentum tensor, and derive explicit coordinate transformations in the near-horizon region. We discuss the appropriate boundary conditions for the embedding of the model into an FRWL background, describe their evaporation in the linear regime, and highlight consequences for the laws of black hole mechanics when back-reaction is present.

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