On quantum traversability of wormholes

TL;DR

This paper investigates the quantum traversability of generalized Ellis-Bronnikov wormholes by analyzing tunneling effects and calculating transmission coefficients for non-relativistic particles using analytical and approximation methods.

Contribution

It provides the first analytical solutions for the Schrödinger equation in this spacetime and explores quantum tunneling through wormholes with different potential barrier configurations.

Findings

Single barrier potential for n=2 at the wormhole throat

Double barrier potential for n≠2 with zero angular momentum

Transmission coefficients derived using delta-barrier approximation

Abstract

In this paper we study the possibility of non-relativistic quantum particles to traverse the generalized Ellis-Bronnikov wormholes by considering quantum effects, such as tunneling. We have used the generalized Ellis-Bronnikov wormhole metric and found that for $n=2$ we have a single barrier shaped effective potential centered at the throat of the wormhole for any value of orbital angular momentum. For $n\neq2$ we have a symmetric double barrier shaped potential when the orbital angular momentum is zero and a single barrier for nonzero angular orbital momentum. Analytical solutions for the Schr\"{o}dinger equation in the generalized Ellis-Bronnikov spacetime could be found only for $n=2$. Such solutions were given in terms of the confluent Heun functions. Finally, by using a delta-barrier approximation we could find the transmission and reflection coefficients for a non-relativistic particle to traverse the generalized Ellis-Bronnikov wormhole.