  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.
