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 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.

Figure 1

The schematic diagram of the effective Higgs potential around evaporating black hole. The backreaction of the Hawking radiation around the black hole stabilizes the Higgs potential at $T_{\mathrm{H}}\gtrsim {\mathrm{\Lambda }}_I$. The figure sets the present best-fit values of $m_h$ and $m_t$, and takes different Hawking temperatures $T_{\mathrm{H}}=10^{9.0}-10^{10.2}\mathrm{GeV}$ for the Higgs potential on Eq. (20).

Figure 2

The Penrose-Carter diagram of the maximally extended Schwarzschild manifold. Regions I or II are asymptotically flat, Region III is the black hole, and Region IV is the white hole. ${\mathcal{H}}^{+}$ corresponds to the (future) black hole horizon, ${\mathcal{H}}^{-}$ is the (past) black hole horizon, ${\mathcal{J}}^{+}$ corresponds to the (future) null infinity, and ${\mathcal{J}}^{-}$ is the (past) null infinity.

Figure 3

The schematic diagram of the effective Higgs potential including higher-order corrections of ${\lambda }_6$, ${\lambda }_8<0$. The back-reaction of the Hawking radiation destabilizes the Higgs potential at $T_{\mathrm{H}}\gtrsim {\mathrm{\Lambda }}_{\mathrm{UV}}$ as shown by Eq. (38) and the second-order transition occurs around the black hole.