|Abstract : ||Astronomical and cosmological observations suggest that the universe is dominated in the form of cold, non-baryonic dark matter. Many experiments to directly detect and study dark matter particles are being actively undertaken, but none have yet succeeded. It has been proposed that the Primordial Black Holes (PBHs) can be a potential dark matter candidate. In a realistic scenario, PBHs which describe the dark matter should be embedded in the cosmological background, surrounded by mass distributions. Therefore, it would be very useful to study exact solutions of the Einstein equations which could describe objects with strong gravitational fields embedded in an expanding universe like in the case of the Sultana-Dyer metric.
In this work, we obtain two the exact time-dependent solution that models evaporating black holes with a matter content described by a two-fluid source. Thus, the solution considers all three aspects of PBHs — Hawking radiation, black hole surrounded by mass distribution, and cosmological background. Our model predicts that the decay rate of the PBHs occurs faster for larger masses; opposite compared to the
black holes in asymptotically flat space-times. Besides that, the invariant quantity such as Misner-Sharp-Hernandez energy, the dynamical horizon, and Kodama vector was studied. (Based on arXiv:2110.14379)|