Electroweak Vacuum Collapse induced by Vacuum Fluctuations of the Higgs
  Field around Evaporating Black Holes
  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 can not 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 PBH abundance
from the vacuum stability. Finally, we show that the high-order corrections of
the BSM or QG would not destabilize the Higgs potential, otherwise even a
single evaporating black hole triggers a collapse of the electroweak vacuum.
