Exact model for evaporating primordial black holes in a cosmological spacetime

Abstract

Primordial black holes (PBHs) in the mass range ${10}^{17}--{10}^{23}\text{ }\text{ }\mathrm{gm}$ are considered as possible dark matter candidates as they are not subject to big-bang nucleosynthesis constraints and behave like cold dark matter. If PBHs are indeed dark matter, they cannot be treated as isolated objects in asymptotic flat space-time. Furthermore, when compared to stellar-mass black holes, the rate at which the Hawking particles radiate out from PBHs is significantly faster. In this work, we obtain an exact time-dependent solution that models evaporating black holes in the cosmological background. As a result, the solution considers all three aspects of PBHs---mass-loss due to Hawking radiation, black hole surrounded by mass distribution, and cosmological background. Furthermore, our model predicts that the decay of PBHs occurs faster for larger masses; however, the decay rate reduces for lower mass. Finally, we discuss the implications of theoretical constraints on PBHs as dark matter.