# Formation threshold of rotating primordial black holes

## TL;DR

This paper derives the density contrast threshold for forming rotating primordial black holes during the radiation-dominated era, highlighting the impact of angular momentum on the formation conditions.

## Contribution

It extends previous non-rotating black hole formation thresholds to include rotation, providing a simple analytical relation based on the Jeans criterion.

## Key findings

- Threshold increases with the square of angular momentum.
- Derived threshold differs from non-rotating case, indicating rotation's significant effect.
- Uncertainties remain, requiring numerical relativity for precise results.

## Abstract

Within the framework that primordial black holes are formed by the direct gravitational collapse of large primordial density perturbations in the radiation dominated stage, we derive the threshold of the density contrast for the formation of rotating primordial black holes based on the simple Jeans criterion. It is found that the threshold value increases in proportion to the square of the angular momentum. We then apply the recently refined analysis on the formation threshold for non-rotating black holes to the case of rotating black holes, and contrast the derived threshold with the former. Caveats and effects ignored in our analysis are also presented, which suggests that the uncertainties of our result can be addressed only by means of numerical relativity.