Abstract
We show that the physical conditions which induce the Thakurta metric,
recently studied by Boehm et al. in the context of time-dependent black hole
masses, correspond to a single accreting black hole in the entire Universe
filled with isotropic non-interacting dust. In such a case, the physics of
black hole accretion is not local but tied to the properties of the entire
Universe. Any density fluctuation or interaction would destroy such a picture.
We do not know any realistic physical example where such conditions can be
realized. In particular, this solution does not apply to black hole binaries.
As cosmological black holes and their mass growth via accretion are not
described by the Thakurta metric, constraints on the primordial black hole
abundance from the LIGO-Virgo and the CMB measurements remain valid.
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