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Black holes don't source fast Higgs vacuum decay
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We argue that the rate of Standard Model vacuum or thermal decay seeded by primordial black holes is negligible (because non-perturbatively suppressed by the small quartic Higgs coupling) and independent of the non-minimal coupling of the Higgs to gravity.
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Thermal false vacuum decay near black holes is aspherical
False vacuum decay near a thermal Schwarzschild black hole is dominated by aspherical critical bubbles for intermediate sizes and by horizon-riding Fubini-Lipatov bounces for large sizes.
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