On catalyzed vacuum decay around a radiating black hole and the crisis of the electroweak vacuum

TL;DR

This paper studies how Hawking radiation from black holes affects false vacuum decay, finding that the decay rate is mostly unaffected unless the scalar field strongly couples to radiation, implying black holes do not significantly catalyze vacuum decay.

Contribution

It provides a detailed analysis of the impact of Hawking radiation on vacuum decay rates around black holes, showing minimal effect unless coupling is extremely large.

Findings

Vacuum decay rate slightly decreases near the horizon due to thermal stabilization.

Decay rate remains largely unchanged unless scalar-radiation coupling is very strong.

Hawking radiation does not significantly prevent Higgs vacuum decay catalyzed by black holes.

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.