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Evolution of primordial black holes in an adiabatic FLRW universe with gravitational particle creation

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Abstract

We study the evolution of primordial black holes (PBHs) in an adiabatic FLRW universe with dissipation due to bulk viscosity which is considered to be in the form of gravitational particle creation. Assuming that the process of evaporation is quite suppressed during the radiation era, we obtain an analytic solution for the evolution of PBH mass by accretion during this era, subject to an initial condition. We also obtain an upper bound on the accretion efficiency \(\epsilon \) for \(a \sim a_r\), where \(a_r\) is the point of transition from the early de Sitter era to the radiation era. Furthermore, we obtain numerical solutions for the mass of a hypothetical PBH with initial mass 100 g assumed to be formed at an epoch when the value of the Hubble parameter was, say, 1 km/s/Mpc. We consider three values of the accretion efficiency, \(\epsilon =0.23,0.5\), and 0.89 for our study. The analysis reveals that the mass of the PBH increases rapidly due to the accretion of radiation in the early stages of its evolution. The accretion continues but its rate decreases gradually with the evolution of the Universe. Finally, Hawking radiation comes into play and the rate of evaporation surpasses the accretion rate so that the PBH mass starts to decrease. As the Universe grows, evaporation becomes the dominant phenomenon, and the mass of the PBH decreases at a faster rate. As argued by Debnath and Paul [101], the evaporated mass of the PBHs might contribute towards the dark energy budget of the late Universe.

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This manuscript has no associated data or the data will not be deposited. [Authors’ comment: Data sharing is not applicable to this article as no new data were created in this study.]

Notes

  1. The lower limit of the integral on the right-hand side is \(a'=a_r/a_r\) which equals 1.

  2. The figure has been produced with Maple 13.

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Acknowledgements

The author S.S. is grateful to Arindam Kumar Chatterjee and Bibekananda Nayak for introducing him to the excitng field of Primordial Black Holes through some informal discussions and also for drawing his attention to some important references in the field. He would also like to thank Ritabrata Biswas for a discussion on black hole accretion.

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Authors and Affiliations

  1. Department of Mathematics, Panihati Mahavidyalaya, Kolkata, West Bengal, 700110, India

    Subhajit Saha

  2. Department of Physics, Vivekananda Satavarshiki Mahavidyalaya (affiliated to the Vidyasagar University), Manikpara, West Bengal, 721513, India

    Abdulla Al Mamon

  3. Department of Mathematics, Sree Chaitanya College, Prafullanagar, Habra, West Bengal, 743268, India

    Somnath Saha

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  1. Subhajit Saha
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Saha, S., Mamon, A.A. & Saha, S. Evolution of primordial black holes in an adiabatic FLRW universe with gravitational particle creation. Gen Relativ Gravit 54, 122 (2022). https://doi.org/10.1007/s10714-022-03010-6

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