Super-slow phase transition catalyzed by BHs and the birth of baby BHs
We discuss the unique phenomenology of first-order phase transitions (FOPTs) catalyzed by primordial black holes (BHs). Because of the enhancement of the vacuum nucleation rate around a BH, vacuum nucleation can be triggered only around BHs. If the average number of BHs within one Hubble volume is smaller than unity at the time of bubble nucleation, each bubble catalyzed around them expands to the Hubble size, and the Hubble patches containing BHs transition to the true vacuum, whereas the rest of the universe remains in the false vacuum. Assuming that the vacuum energy difference is negligible in relation to the total energy until a time close to the bubble collision, most false-vacuum patches do not undergo inflation, and the entire universe is eventually filled with true-vacuum bubbles much after BH formation and bubble nucleation. This "super-slow phase transition" scenario predicts enhanced gravitational wave signals from bubble collisions and can be tested in future observations. Moreover, a small fraction of the universe remains in the false vacuum and inflates by chance, and the corresponding region can be seen as a BH from an outside observer. This scenario of "birth of baby BHs from parent BHs" via the catalyzed phase transition can account for the entire dark matter in our universe.