In this paper, we discuss the Higgs vacuum stability around evaporating black holes. We provide a new approach to investigate the false vacuum decay around the black hole and clearly show how vacuum fluctuations of the Higgs induce a gravitational collapse of the vacuum. Furthermore, we point out that the backreaction of the Hawking radiation cannot be ignored and the gravitational vacuum decay is exponentially suppressed. However, a large number of the evaporating (or evaporated) primordial black holes threaten the existence of the Universe and we obtain a new upper bound on the evaporating primordial black hole abundance from the vacuum stability. Finally, we show that the high-order corrections of the beyond standard model or quantum gravity would not destabilize the Higgs potential, otherwise even a single evaporating black hole triggers a collapse of the electroweak vacuum.
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