# Spin of Primordial Black Holes

## TL;DR

This paper demonstrates that primordial black holes are nearly non-rotating at first order in primordial fluctuations, with their spin arising only at second order, leading to very small expected spin parameters.

## Contribution

The study shows that the primordial black hole spin vanishes at first order in fluctuations and identifies the quadratic contribution to the spin from ambient acoustic waves.

## Key findings

- Spin vanishes at first order in primordial fluctuations.
- Quadratic contribution to black hole spin from ambient acoustic waves.
- Estimated spin parameter at formation is at the percent level.

## Abstract

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