Primordial black holes have attracted intense attention as it has been revealed that a considerable fraction of binary black holes discovered by gravitational wave observations by LIGO and Virgo have masses in the range of several tens of solar masses. In fact, it is proposed that such very massive black holes might be of cosmological origin. In order to discuss physical properties of primordial black holes several authors recently adopted the Thakurta metric. But, Gert Hutsi et al. & Harada et al. now terminated this controversy by arguing that the Thakurta metric does not describe cosmological black holes.

Hutsi et al. clarified that the mass growth of Thakurta black holes (BHs) is due to an influx of energy (i.e. accretion), which, by definition, is not a feature of geometry. In other words, Thakurta metric describes accreting BHs whose mass grows proportional to scale factor (a) and that must be accompanied by a smooth dark matter component which the BHs can accrete.

“We showed that the average energy density of primordial Thakurta black holes scales as a¯^{2}and requires an unrealistic and fine-tuned energy transfer from a smooth dark matter component to the primordial black hole sector.”— told Gret Hutsi, senior researcher, Tartu Observatory and first author of the study

While, Harada and colleagues recently showed 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.

**References***: (1) Gert Hütsi, Tomi Koivisto, Martti Raidal, Ville Vaskonen, Hardi Veermäe, “Reply to “Comment on: Cosmological black holes are not described by the Thakurta metric”, Arxiv, pp. 1-2, 2021. https://arxiv.org/abs/2106.02007 (2) Tomohiro Harada, Hideki Maeda, Takuma Sato, “Thakurta metric does not describe a cosmological black hole”, Arxiv, pp. 1-4, 2021. https://arxiv.org/abs/2106.06651*

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