Spin of primordial black holes

Primordial black holes, formed from rare peaks in the primordial fluctuations ζ, are non-rotating if the RMS (root mean square) fluctuation ζ_rms is sent to zero. We show that the spin also vanishes at first order in ζ_rms, suggesting the dimensionless spin parameter a_rms ∼ ζ_rms ². We identify one quadratic contribution to the spin by calculating (and extrapolating to the formation time) the torque on a black hole due to ambient acoustic waves. For a reasonable density of primordial black holes this implies a percent level spin parameter.