Note on the Stabilities of the Light-like Galileon Solutions

TL;DR

This paper re-examines the stability of light-like galileon solutions, emphasizing the importance of finite energy conditions and clarifying ghost instabilities, challenging previous local approximation results.

Contribution

It provides an exact linear stability analysis of light-like galileon solutions, highlighting the role of finite energy conditions and addressing misconceptions about zero-mode arguments.

Findings

Finite energy condition is crucial for stability.

Exact analysis reveals potential ghost instabilities.

Zero-mode argument does not directly apply to light-like solitons.

Abstract

Light-like galileon solutions have been used to investigate the chronology problem in galileon-like theories, and in some cases may also be considered as solitons, evading a non-existence constraint from a zero-mode argument. Their stabilities have been analyzed via "local" approximation, which appears to suggest that all these light-like solutions are stable. We re-analyze the stability problem by solving the linear perturbation equation \emph{exactly}, and point out that the finite energy condition is essential for the light-like solitons to be stable. We also clarify potential ghost instabilities and why the zero-mode argument can not be naively generalized to include the light-like solitons.