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 ζrms is sent to zero. We show that the spin also vanishes at first order in ζrms, suggesting the dimensionless spin parameter arms∼ζrms2. 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.