Spins of primordial black holes formed with a soft equation of state

Understand

We investigate the probability distribution of the spins of primordial black holes (PBHs) formed in the universe dominated by a perfect fluid with the linear equation of state $p=w\rho$, where $p$ and $\rho$ are the pressure and energy density of the fluid, respectively.

• We particularly focus on the parameter region $0<w\leq 1/3$ since the larger value of the spin is expected for the softer equation of state than that of the radiation fluid ($w=1/3$).
• The angular momentum inside the collapsing region is estimated based on the linear perturbation equation at the turn-around time which we define as the time when the linear velocity perturbation in the conformal Newtonian gauge takes the minimum value.
• The probability distribution is derived based on the peak theory with the Gaussian curvature perturbation.