  Recently, the Thakurta metric has been adopted as a model of primordial black
holes. We show that the spacetime described by this metric has neither
black-hole event horizon nor black-hole trapping horizon and involves the
violation of all the standard energy conditions as a solution of the Einstein
equation. Therefore, this metric does not describe a cosmological black hole in
the early universe. It is pointed out that a contradictory claim by the other
group stems from an incorrect choice of sign.
