Black hole induced false vacuum decay from first principles

TL;DR

This paper develops a method to calculate black hole-induced false vacuum decay rates using complex tunneling solutions, revealing different decay behaviors across various quantum vacua and their dependence on black hole temperature.

Contribution

It introduces a first-principles approach to evaluate false vacuum decay near black holes, accounting for boundary conditions and vacuum structures in a novel way.

Findings

Decay rates differ significantly between vacua.

Unruh vacuum decay is exponentially suppressed at low temperatures.

Decay suppression diminishes at high black hole temperatures.

Abstract

We provide a method to calculate the rate of false vacuum decay induced by a black hole. The method uses complex tunneling solutions and consistently takes into account the structure of different quantum vacua in the black hole metric via boundary conditions. The latter are connected to the asymptotic behavior of the time-ordered Green's function in the corresponding vacua. We illustrate the technique on a two-dimensional toy model of a scalar field with inverted Liouville potential in an external background of a dilaton black hole. We analytically derive the exponential suppression of tunneling from the Boulware, Hartle-Hawking and Unruh vacua and show that they are parametrically different. The Unruh vacuum decay rate is exponentially smaller than the decay rate of the Hartle-Hawking state, though both rates become unsuppressed at high enough black hole temperature. We interpret the vanishing suppression of the Unruh vacuum decay at high temperature as an artifact of the two-dimensional model and discuss why this result can be modified in the realistic case of black holes in four dimensions.