Exact model for evaporating primordial black holes in a cosmological spacetime

Primordial black holes (PBHs) in the mass range ${10}^{17}–{10}^{23}\mathrm{gm}$ 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.

Figure 1

Left: plot of rate of change of mass with time versus $\mathcal{M}$. Right: plot of $\mathcal{M}$ as a function of $\tau$ for Schwarzschild for Schwarzschild (44) and cosmological black hole (46).

Figure 2

Left: plot of the Ricci scalar $(R(\tau ))$ vs $\tau$ for the branch I (c1)for $0.95\le \tau \le 1,m=M_0$ and for the branch II (c3) $1.0\le \tau \le 3,m=-M_0$. Right: plot of the Ricci scalar $(R(\tau ))$ vs $\tau$ for the branch I (c1)for $0.85\le \tau \le 1,m=M_0$ and for the branch II (c3) $1.0\le \tau \le 3,m=M_0$.