Thakurta metric does not describe a cosmological black hole

TL;DR

The paper demonstrates that the Thakurta metric, previously used to model primordial black holes, does not actually describe a black hole due to the absence of horizons and violation of energy conditions.

Contribution

It clarifies that the Thakurta metric cannot represent a cosmological black hole and corrects a misconception caused by an incorrect sign choice in prior work.

Findings

No event horizon or trapping horizon in the Thakurta metric

Violates all standard energy conditions

Does not describe a black hole in the early universe

Abstract

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.