On thermal false vacuum decay around black holes

TL;DR

This paper argues that in black hole catalyzed false vacuum decay, only time-independent thermal jump solutions are relevant, extending previous understanding from flat space to black hole environments without relying on thin-wall approximation.

Contribution

It demonstrates that only time-independent solutions drive black hole catalyzed false vacuum decay, applicable to various black hole types and multi-field theories, without thin-wall assumptions.

Findings

Time-independent solutions dominate decay process.

Applicable to diverse black hole geometries.

No thin-wall approximation needed.

Abstract

In flat space and at finite temperature, there are two regimes of false vacuum decay in quantum field theory. At low temperature, the decay proceeds through thermally-assisted tunneling described by periodic Euclidean solutions -- bounces -- with non-trivial time dependence. On the other hand, at high temperature the bounces are time-independent and describe thermal jumps of the field over the potential barrier. We argue that only solutions of the second type are relevant for false vacuum decay catalyzed by a black hole in equilibrium with thermal bath. The argument applies to a wide class of spherical black holes, including $d$-dimensional AdS/dS-Schwarzschild black holes and Reissner-Nordstr\"om black holes sufficiently far from criticality. It does not rely on the thin-wall approximation and applies to multi-field scalar theories.