Probing the Ellis-Bronnikov wormhole geometry with a scalar field: clouds, waves and Q-balls

TL;DR

This paper investigates scalar field behavior in the Ellis-Bronnikov wormhole, revealing solutions for clouds, waves, and Q-balls, and addressing discontinuities with self-interactions.

Contribution

It provides exact solutions for scalar fields in wormhole backgrounds and demonstrates the existence of stable Q-balls with self-interaction.

Findings

Exact solutions in terms of Heun's functions

Discontinuity issues in scalar clouds addressed by self-interactions

Existence of spherically symmetric and spinning Q-balls

Abstract

The Ellis-Bronnikov solution provides a simple toy model for the study of various aspects of wormhole physics. In this work we solve the Klein-Gordon equation in this background and find an exact solution in terms of Heun's function. This may describe 'scalar clouds' ($i.e.$ localized, particle-like configuration) or scalar waves. However, in the former case, the radial derivative of the scalar field is discontinuous at the wormhole's throat (except for the spherical case). This pathology is absent for a suitable scalar field self-interaction, and we provide evidence for the existence of spherically symmetric and spinning Q-balls in a Ellis-Bronnikov wormhole background.