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Dark Matter and Dark Radiation from Evaporating Kerr Primordial Black Holes

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Abstract

The mechanism of generation of dark matter and dark radiation from the evaporation of primordial black holes is very interesting. We consider the case of Kerr black holes to generalize previous results obtained in the Schwarzschild case. For dark matter, the results do not change dramatically, and the bounds on warm dark matter apply similarly: in particular, the Kerr case cannot save the scenario of black hole domination for light dark matter. For dark radiation, the expectations for \(\Delta N_{\textrm{eff}}\) do not change significantly with respect to the Schwarzschild case, but for an enhancement in the case of spin 2 particles: in the massless case, however, the projected experimental sensitivity would be reached only for extremal black holes.

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Notes

  1. It is interesting to compare our numerical result with a previous analytical approximation, valid in the Schwarzschild case [7], \(cp_{\textrm{ev}}\approx\langle E_{X}(t_{\textrm{ev}})\rangle\approx 6\,k_{B}T^{S}_{\textrm{BH}}\).

  2. It is reasonable to assume that the entropy is conserved from matter-radiation equality to the present time, so that \(\alpha\approx\alpha^{\prime}\).

  3. A more sophisticated analysis should follow the lines of [27].

  4. If the warm particles decouple when they are relativistic, their momentum distribution function remains constant until gravitational clustering begins. All particle momenta scale as \(a^{-1}\), which we can describe by scaling their temperature \(T_{W}\) accordingly. When the particles become nonrelativistic, we can use \(p=m_{W}v_{W}\).

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NOTE ADDED

After this work was submitted, a related work by Arbey et al. [49] was posted, which confirmed and further extended our results.

After this work was submitted, a related work by Arbey et al. [49] was posted, which confirmed and further extended our results.

FUNDING

I.M. acknowledges partial support by the research project TAsP (Theoretical Astroparticle Physics) funded by the Istituto Nazionale di Fisica Nucleare (INFN).

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  1. Dip. di Fisica e Scienze della Terra, Ferrara University and INFN, Ferrara, Italy

    Isabella Masina

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Masina, I. Dark Matter and Dark Radiation from Evaporating Kerr Primordial Black Holes. Gravit. Cosmol. 27, 315–330 (2021). https://doi.org/10.1134/S0202289321040101

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