If vacuum decay is triggered, it will spread (at maximum) at the speed of light. But the spacetime inside a black hole is causally disconnected from the space outside. Nothing that happens inside the event horizon can influence anything that happens outside. Therefore it can be assumed that a vacuum decay cannot escape from inside of a black hole. But is it really the case? What happens when the black hole finally evaporates? Is the vacuum decay released into the rest of the universe?
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$\begingroup$ vacuum decay occurs in the frame of quantum mechanics. en.wikipedia.org/wiki/False_vacuum_decay Gravity is not yet definitively quantized so as to be able to estimate possible vacuums inside a black hole. $\endgroup$– anna vCommented Nov 14, 2021 at 6:53
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$\begingroup$ So we'd need a working model of quantum gravity to answer this question? $\endgroup$– zucculentCommented Nov 14, 2021 at 7:09
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$\begingroup$ for sure. Take the Higgs mechanism which is the metastable vacuum we know about and the theory fits the data and is predictive. An equivalent metastable vacuum should exist for gravity in order to be able to talk of vacuum decay for gravity. $\endgroup$– anna vCommented Nov 14, 2021 at 7:15
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1$\begingroup$ If a vacuum decay happens tomorrow, can it affect anything today? The same question rephrased. $\endgroup$– safesphereCommented Nov 14, 2021 at 14:55
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2$\begingroup$ @annav: I think the OP is talking about the vacuum decay of some other field that happens to be present in all of space—including inside the black hole. (Such as the Higgs.) They're not asking about some kind of false vacuum of GR itself. If they're interested in the former case, then it's perfectly possible to answer the question so long as spacetime can be treated classically, which will be the case inside the black hole except near the singularity. $\endgroup$– Michael SeifertCommented Nov 15, 2021 at 19:11
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