Spins of primordial black holes formed in the matter-dominated phase of the Universe

TL;DR

This paper investigates how angular momentum influences the formation and spin of primordial black holes during a matter-dominated phase, revealing that most PBHs are rapidly rotating and that matter domination enhances their production despite suppression effects.

Contribution

It provides a detailed analysis of the effects of angular momentum and anisotropy on PBH formation and spin, including estimates of production rates under various conditions.

Findings

Most PBHs formed are rapidly rotating near the extremal spin limit.

Angular momentum causes suppression of PBH production at small density fluctuations.

Matter-dominated phase enhances PBH production despite suppression effects.

Abstract

Angular momentum plays very important roles in the formation of PBHs in the matter-dominated phase if it lasts sufficiently long. In fact, most collapsing masses are bounced back due to centrifugal force, since angular momentum significantly grows before collapse. As a consequence, most of the formed PBHs are rapidly rotating near the extreme value $a_{*}=1$, where $a_{*}$ is the nondimensional Kerr parameter at their formation. The smaller the density fluctuation $\sigma_{H}$ at horizon entry is, the stronger the tendency towards the extreme rotation. Combining the effect of angular momentum with that of anisotropy, we estimate the black hole production rate. We find that the production rate suffers from suppression dominantly due to angular momentum for a smaller value of $\sigma_{H}$, while due to anisotrpopy for a larger value of $\sigma_{H}$. We argue that matter domination significantly enhances the production of PBHs despite the suppression. If the matter-dominated phase does not last so long, the effect of the finite duration significantly suppresses PBH formation and weakens the tendency towards large spins. (abridged)