Extreme-value statistics of the spin of primordial black holes

How rare are extreme-spin primordial black holes? We show how, from an underlying distribution of PBH spin, extreme-value statistics can be used to quantify the rarity spinning PBHs with Kerr parameter close 1. Using Peaks-Over-Threshold method, we how probability that a forms spin exceeding sufficiently high threshold calculated using Generalised Pareto Distribution. This allows us estimate average number amongst which find single formed threshold. found gives rise exceedingly near-extremal at formation time: for typical values, roughly up one in hundred million would Thorne limit. discuss conditions under even more may produced, including modifying skewness and kurtosis via smooth transformation. deduce our calculations that, if indeed asteroid-mass above current observational limit on evaporating mass ~10^{17} g contribute significantly dark matter, it is likely some them could PBHs.