False vacuum decay catalyzed by black hole in a heat bath

TL;DR

This paper investigates how black holes can catalyze false vacuum decay in a two-dimensional scalar field model, revealing both quantum tunneling and stochastic activation mechanisms relevant to early universe cosmology.

Contribution

It introduces a simplified 2D model to analyze black hole-induced vacuum decay, including non-equilibrium states and non-thermal sphalerons, extending understanding beyond equilibrium scenarios.

Findings

Decay suppression evaluated for small field excitations.

Decay via stochastic activation with non-thermal sphalerons identified.

Results applicable to primordial black hole effects in early universe.

Abstract

We study false vacuum decay catalyzed by black holes. We consider a scalar field model with unstable potential in the background of a dilaton black hole in two dimensions. The model reproduces many features of the Schwarzschild black hole background in four dimensions, including the centrifugal barrier for linearized field perturbations. We study decays from the non-equilibrium state describing the evaporating black hole immersed in the thermal bath with a different temperature. We analytically construct the tunneling solution relevant at small field excitations and evaluate the decay suppression. We show how they reduce to those for the Hartle-Hawking (equilibrium) and Unruh states in the corresponding limits. For large field excitations the decay proceeds via stochastic activation; we find the relevant non-thermal sphaleron configuration in a certain region of parameters of the model and construct the semiclassical solution describing tunneling onto this sphaleron. Our results provide insights into the vacuum decay induced by small primordial black holes in the radiation-dominated era of the universe.