An exact model for evaporating primordial black holes in cosmological space-time

TL;DR

This paper presents an exact, time-dependent model for evaporating primordial black holes within a cosmological setting, accounting for mass loss, surrounding matter, and the universe's expansion, with implications for dark matter research.

Contribution

It introduces a novel exact solution for evaporating black holes in cosmological space-time, integrating mass loss, environmental effects, and cosmic expansion.

Findings

PBH decay rate is faster for larger masses

Decay rate decreases for lower mass PBHs

Model aligns with dark matter constraints

Abstract

Primordial black holes (PBHs) in the mass range $10^{17} - 10^{23}~{\rm gm}$ 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, \emph{the decay rate reduces for lower mass}. Finally, we discuss the implications of theoretical constraints on PBHs as dark matter.