Can black holes nucleate vacuum phase transitions?

The decay of false-vacuum states through a first-order phase transition in the presence of a Schwarzschild black hole is studied in the zero-temperature limit. The equations of motion for a thin-wall bubble which forms in a spherically symmetric fashion around a Schwarzschild–de Sitter (or –anti–de Sitter) black hole are derived. The Euclidean action for these bubble solutions is calculated and is found to be smaller, by up to a factor of roughly 2, than the O(4)-symmetric action in which no black hole is present. It thus appears that a black hole can act as an effective nucleation center for a first-order vacuum phase transition. It will then be more difficult (require more ‘‘fine-tuning’’ of the potential) than was previously believed to achieve supercooling of a false-vacuum state, provided that appropriate-mass black holes are present.