Phase transition catalyzed by primordial black holes

We investigate the first-order phase transition catalyzed by primordial black holes~(PBHs) in the early Universe. We find that super-horizon curvature perturbations generated in this scenario lead to the production of gravitational waves when the scalar modes re-enter the horizon. If PBHs with masses about ${10}^{-13}{M}_{\odot }$ constitute all dark matter, the first-order electroweak phase transition catalyzed by PBHs can explain the gravitational wave signal observed by pulsar timing array collaborations without the overproduction of PBHs.