Thakurta metric does not describe a cosmological black hole

Understand

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.