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We show that the physical conditions which induce the Thakurta metric,recently studied by B{\oe}hm {\it et al.} in the context of time-dependentblack hole masses, correspond to a single accreting black hole in the entireUniverse filled with isotropic non-interacting dust. In such a case, thephysics of black hole accretion is not local but tied to the properties of thewhole Universe. We show that radiation, primordial black holes or particle darkmatter cannot produce the specific energy flux required for supporting the massgrowth of Thakurta black holes. In particular, this solution does not apply toblack hole binaries. We conclude that cosmological black holes and their massgrowth cannot be described by the Thakurta metric, and thus existingconstraints on the primordial black hole abundance from the LIGO-Virgo and theCMB measurements remain valid.

Cosmological black holes are not described by the Thakurta metric: LIGO-Virgo bounds on PBHs remain unchanged