  Black hole entropy is a robust prediction of quantum gravity with no
established phenomenological consequences to date. We use the
Bekenstein-Hawking entropy formula and general-relativistic statistical
mechanics to determine the probability distribution of random geometries
uniformly sampled in phase space. We show that this statistics (in the limit
$\hbar\to 0$) is relevant to large curvature perturbations, resulting in a
population of primordial black holes with zero natal spin. In principle, the
identification of such a population at LIGO, Virgo, and future gravitational
wave observatories could provide the first observational evidence for the
statistical nature of black hole entropy.
