Black holes initiate false-vacuum decay

We consider O(3)-invariant tunneling processes which induce false-vacuum decay in general relativity. We find that in the presence of a black hole in a false vacuum the process of spontaneous nucleation of a bubble around a black hole (with the true phase in between the bubble shell and the black-hole surface) proceeds at a tremendously faster rate than that of an empty O(4)-invariant true phase bubble provided the black-hole mass does not exceed $m_{max}=\frac{M_{\mathrm{Pl}}^4}{12\sqrt{3}\pi S}$. There we also find the spontaneous creation of black holes during first-order vacuum-vacuum phase transitions.