Propagation of Test Particles and Scalar Fields on a Class of Wormhole Space-Times

TL;DR

This paper investigates how test particles and scalar fields propagate through a specific class of wormhole space-times, analyzing geodesic behavior, stability of scalar fields, and the impact of coupling constants.

Contribution

It provides a detailed numerical and analytical study of geodesic trajectories and scalar field stability on wormholes, clarifying the role of coupling constants in field behavior.

Findings

Geodesics can traverse, reflect, or be captured by wormholes depending on initial conditions.

Scalar fields are stable only for certain coupling constants.

Pathological behaviors in scalar self-interactions are due to non-stable coupling regimes.

Abstract

In this paper, we consider the problem of test particles and test scalar fields propagating on the background of a class of wormhole space-times. For test particles, we solve for arbitrary causal geodesics in terms of integrals which are solved numerically. These integrals are parametrized by the radius and shape of the wormhole throat as well as the initial conditions of the geodesic trajectory. In terms of these parameters, we compute the conditions for the geodesic to traverse the wormhole, to be reflected by the wormhole's potential or to be captured on an unstable bound orbit at the wormhole's throat. These causal geodesics are visualized by embedding plots in Euclidean space in cylindrical coordinates. For massless test scalar fields, we compute transmission coefficients and quasi-normal modes for arbitrary coupling of the field to the background geometry in the WKB approximation. We show that solutions of the scalar wave equation on this class of wormholes are stable only for certain values of the coupling constant. This analysis is interesting since recent computations of self-interactions of a static scalar field in wormhole space-times reveal some anomalous dependence on the coupling constant such as the existence of an infinite discrete set of poles. We show that this pathological behavior of the self-field is an artifact of computing the interaction for values of the coupling constant that do not lie in the domain of stability.