Pathology in WKB wave function for tunneling assisted by gravity

TL;DR

This paper discusses challenges in applying the WKB approximation to gravity-assisted tunneling processes, highlighting specific pathological issues in various quantum gravitational tunneling scenarios.

Contribution

It identifies and analyzes specific pathologies in the WKB wave function construction for gravity-influenced tunneling processes, a novel insight into quantum gravity effects on tunneling.

Findings

Pathologies arise in WKB wave functions for gravity-assisted tunneling.

Examples include true vacuum decay, black hole catalyzed false vacuum decay, and black hole/wormhole tunneling.

Challenges in describing quantum fluctuations around semi-classical paths.

Abstract

There are several exotic tunneling processes that can be realized only by incorporating the effect of gravity. Here, we point out that we encounter difficulties in constructing the WKB wave function, once we try to describe quantum fluctuations around the semi-classical tunneling path. We present examples of pathology in the true vacuum decay/upward tunneling, the false vacuum decay catalyzed by a black hole and the tunneling with black hole/wormhole production.