  False vacuum states are metastable in quantum field theories, and true vacuum
bubbles can be nucleated due to the quantum tunneling effect. It was recently
suggested that an evaporating black hole (BH) can be a catalyst of bubble
nucleations and dramatically shortens the lifetime of the false vacuum. In
particular, in the context of the Standard Model valid up to a certain energy
scale, even a single evaporating BH may spoil the successful cosmology by
inducing the decay of our electroweak vacuum. In this paper, we reinterpret
catalyzed vacuum decay by BHs, using an effective action for a thin-wall bubble
around a BH to clarify the meaning of bounce solutions. We calculate bounce
solutions in the limit of a flat spacetime and in the limit of negligible
backreaction to the metric, where it is much easier to understand the physical
meaning, and compare these results with the full calculations done in the
literature. As a result, we give a physical interpretation of the enhancement
factor: it is nothing but the probability of producing states with a finite
energy. This makes it clear that all the other states such as plasma should
also be generated through the same mechanism, and calls for finite-density
corrections to the tunneling rate which tend to stabilize the false vacuum. We
also clarify that the dominant process is always consistent with the
periodicity indicated by the BH Hawking temperature after summing over all
possible remnant BH masses or bubble energies, although the periodicity of each
bounce solution as a function of a remnant BH can be completely different from
the inverse temperature of the system as mentioned in the previous literature.
