Spin of Primordial Black Holes

Primordial black holes, formed from rare peaks in the primordial fluctuations $ζ$, are non-rotating at zeroth order in $ζ_{\rm rms}$. We show that the spin also vanishes at first order in $ζ_{\rm rms}$, suggesting the dimensionless spin parameter $a_{\rm rms} \sim ζ_{\rm rms}^2$. 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.

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