The propagation of particles and fields in wormhole geometries

TL;DR

This paper investigates the behavior of particles and fields in static, spherically symmetric wormhole geometries, revealing stable scalar field propagation but instability in certain matter configurations.

Contribution

It provides a detailed analysis of geodesic trapping, stability of scalar fields, and instability of wormholes sourced by mixed scalar fields, advancing understanding of wormhole physics.

Findings

Existence of trapped null geodesics near the wormhole throat.

Stability of test scalar fields on wormhole backgrounds.

Instability of wormholes sourced by mixed ghost and Klein-Gordon scalar fields.

Abstract

We discuss several properties of static, spherically symmetric wormholes with particular emphasis on the behavior of causal geodesics and the propagation of linear fields. We show there always exist null geodesics which are trapped in a region close to the throat. Depending upon the detailed structure of the wormhole geometry, these trapped geodesics can be stable, unlike the case of the Schwarzschild black hole. We also show that test scalar fields propagating on such wormholes are stable. However, when a mixture of ghost and Klein-Gordon scalar fields is used as a source of the Einstein equations we prove that the resulting static, spherically symmetric wormhole configurations are linearly unstable.