Dirac and Majorana neutrino signatures of primordial black holes

We study Primordial Black Holes (PBHs) as sources of massive neutrinos via Hawking radiation. Under the hypothesis that black holes emit neutrino mass eigenstates, we describe quantitatively how the PBH evolution and lifetime is affected by the mass and fermionic -- Dirac or Majorana -- nature of neutrinos. In the case of Dirac neutrinos, PBHs radiate right-handed and left-handed neutrinos in equal amounts, thus possibly increasing the effective number of neutrino species, $N_{\rm eff}$. Assuming an initially monochromatic PBH mass spectrum, with the initial mass $M_i$ related to the particle horizon mass, and considering the current constraint on $N_{\rm eff}$, we derive a bound on the initial PBH fraction $\beta^\prime$ in the interval $4.3\times 10^7\ {\rm g}\lesssim M_i \lesssim 10^9$ g. Future measurements of $N_{\rm eff}$ may be able to constraint the initial fraction for black hole masses as low as 1 g. If an excess in $N_{\rm eff}$ is found, PBHs with Dirac neutrinos could provide a minimal explanation of it. For example, for $10^7\ {\rm g} \lesssim M_i\lesssim 10^9$ g and $\beta^\prime \gtrsim 10^{-13}$, an excess radiation at the level of $0.2\lesssim \Delta N_{\rm eff}\lesssim 0.37$ is produced, which can alleviate the tension of the Hubble parameter measurements. Finally, we obtain the diffuse flux of right-helical neutrinos from PBHs at the Earth, and show that their detection in a PTOLEMY-like detector (using neutrino capture on tritium) would be difficult.