Thakurta metric does not describe a cosmological black hole
  Recently, the Thakurta metric has been adopted as a model of primordial black
holes by several authors. 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 the null energy condition as a solution of the
Einstein equation. Therefore, this metric does not describe a cosmological
black hole in the early universe.
