Black hole induced false vacuum decay: The role of greybody factors

TL;DR

This paper investigates how black holes influence false vacuum decay, showing that the decay probability varies with black hole states and remains suppressed in radiating black holes, with implications for four-dimensional black holes.

Contribution

It introduces a toy model with greybody factors to analytically study black hole catalyzed false vacuum decay, highlighting differences between Hartle-Hawking and Unruh states.

Findings

Decay rate computed analytically for different black hole states.

Decay probability suppressed in Unruh vacuum at all temperatures.

Results suggest similar behavior in four-dimensional black holes.

Abstract

We study false vacuum decay catalyzed by black holes. We consider a toy two-dimensional model of a scalar field with an unstable potential in the background of a dilaton black hole. A realistic black hole in four dimensions possesses the potential barrier for linear field perturbations. We model this barrier -- the greybody factor -- for spherically-symmetric perturbations in the toy model by adding a coupling between the scalar field and dilaton. We compute analytically the decay rate for the black hole in thermal equilibrium (Hartle-Hawking state) and for the radiating black hole in empty space (Unruh state). Our results show that, contrary to the Hartle-Hawking vacuum, the decay probability of the Unruh vacuum remains exponentially suppressed at all black hole temperatures. We argue that this result holds also in four dimensions.