Abstract
False vacuum decay is a key feature in quantum field theories and exhibits a distinct signature in the early Universe cosmology. It has recently been suggested that the false vacuum decay is catalyzed by a black hole (BH), which might cause the catastrophe of the Standard Model Higgs vacuum if primordial BHs are formed in the early Universe. We investigate vacuum phase transition of a scalar field around a radiating BH with taking into account the effect of Hawking radiation. We find that the vacuum decay rate slightly decreases in the presence of the thermal effect since the scalar potential is stabilized near the horizon. However, the stabilization effect becomes weak at the points sufficiently far from the horizon. Consequently, we find that the decay rate is not significantly changed unless the effective coupling constant of the scalar field to the radiation is extremely large. This implies that the change of the potential from the Hawking radiation does not help prevent the Standard Model Higgs vacuum decay catalyzed by a BH.
Highlights
JHEP08(2020)088 inflationary Universe [21,22,23]
We can see that the thermal correction does not change the phase transition rate practically and the bubble nucleation rate is larger than the black hole (BH) evaporation rate for smaller BH mass with M+ 107, which means that the Higgs vacuum decay would be inevitable if microscopic BHs exist in the Universe
It has been discussed that a small BH, whose mass is smaller than M+ < 107, catalyzes the bubble nucleation in a false vacuum of the Higgs field and its decay rate is evaluated by the bounce action with the zero-temperature potential [26,27,28] and that the rate can be significantly higher than the CdL decay rate
Summary
We start with the review of vacuum phase transition around a Schwarzschild BH following ref. [28].
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