Neutrino primordial Planckian black holes

Extremal rotating black holes can be formed in the Planck energy scattering of Dirac spin parallel neutrinos in the mass state m2 (assuming m1=0), owing to the repulsive interaction between their magnetic dipoles, induced by vacuum fluctuations. Assuming that some recent results of loop-quantised Schwarzschild black holes would be also applicable for the Kerr case, we show that the resulting black hole has Planck mass and angular momentum ħ, and that its horizon area is in the spectrum of the Loop Quantum Gravity area operator. Moreover, we argue that such black holes could be produced at the reheating, with an abundance that allows their interpretation as forming the presently observed dark matter component, provided that the energy scale at inflation is ≈1017 GeV. This scale can be lower if we attribute a high chemical potential to primordial neutrinos. As extremal black holes have zero surface gravity, there is no limits on their abundance from Hawking evaporation.