Radiative losses decelerate black hole-induced true vacuum bubbles in thin-wall phi^4 and sine-Gordon models, ensuring the catalyzed decay rate remains exponentially suppressed.

False vacuum decay is a process where the universe's current state, which is not the lowest energy state, could tunnel to a true vacuum state with lower energy. This is usually very slow due to the need to tunnel through an energy barrier. Black holes, through their Hawking radiation, have high temperatures when small, which could in principle boost the creation of bubbles of true vacuum that expand and convert the false vacuum. In this work, the authors consider two specific field theory models: the phi to the fourth power model and the sine-Gordon model. They focus on the thin-wall limit where the transition between false and true vacuum happens over a thin surface. Their key insight is that as these bubbles are produced near black holes and start expanding at high speeds, they lose energy by emitting radiation. This energy loss slows the bubbles down, preventing them from expanding fast enough to cause a rapid, unsuppressed decay of the vacuum across the universe. As a result, even though black holes might increase the chance of bubble production compared to no black holes, the overall rate remains exponentially small. This means the vacuum decay is still suppressed, addressing concerns about potential instability in the early universe when black holes were more common.