Redshift Effects in Particle Production from Kerr Primordial Black Holes

When rotating primordial black holes evaporate via Hawking radiation, their rotational energy and mass are dissipated with different dynamics. We investigate the effect of these dynamics on the production of dark radiation -- in the form of hot gravitons or vector bosons -- and non-cold dark matter. Although the production of higher-spin particles is enhanced while primordial black holes are rotating, we show that the energy density of dark radiation experiences an extra redshift because their emission effectively halts before PBH evaporation completes. We find that taking this effect into account leads to suppression by a factor of $\mathcal{O}(10)$ of $\Delta N_{\rm eff}$ for maximally rotating black holes as compared to previous results. Using the solution of the Friedmann and Boltzmann equations to accurately calculate the evolution of linear perturbations, we revisit the warm dark matter constraints for light candidates produced by evaporation and how these limits vary over black hole spins. Due to the interplay of enhanced production and late dilution, we obtain that higher spin particles are most affected by these bounds. Our code FRISBHEE, FRIedmann Solver for Black Hole Evaporation in the Early universe, developed for this work can be found at https://github.com/yfperezg/frisbhee