Caustics for Spherical Waves

TL;DR

This paper investigates caustic formation in shift-symmetric scalar field theories with spherical symmetry, identifying specific Galileon models that inherently avoid caustics and linking this to their underlying symmetries.

Contribution

It demonstrates that the pure Galileon, DBI-Galileon, and extreme-relativistic Galileon are uniquely caustic-free for simple $SO(p)$-waves, revealing a symmetry-based criterion.

Findings

Pure Galileon, DBI-Galileon, and extreme-relativistic Galileon are caustic-free.

Caustic-free condition linked to global Galilean or relativistic symmetries.

Identifies symmetry principles underlying caustic avoidance in scalar theories.

Abstract

We study the development of caustics in shift-symmetric scalar field theories by focusing on simple waves with an $SO(p)$-symmetry in an arbitrary number of space dimensions. We show that the pure Galileon, the DBI-Galileon, and the extreme-relativistic Galileon naturally emerge as the unique set of caustic-free theories, highlighting a link between the caustic-free condition for simple $SO(p)$-waves and the existence of either a global Galilean symmetry or a global (extreme-)relativistic Galilean symmetry.