A Galileon Primer

TL;DR

This paper introduces the fundamental aspects of galileon models, exploring their equations, solutions, and gravitational effects, including shock fronts and singularities, providing a comprehensive primer for understanding galileons in flat and curved spacetimes.

Contribution

It develops a general formalism for galileon models, discusses duality, constructs solutions, and analyzes their gravitational effects, including singularities and horizons.

Findings

Existence of galileon shock fronts conjectured.

Solutions with naked singularities identified.

Critical boundary data separating different solution types.

Abstract

Elementary features of galileon models are discussed at an introductory level. Following a simple example, a general formalism leading to a hierarchy of field equations and Lagrangians is developed for flat spacetimes. Legendre duality is discussed. Implicit and explicit solutions are then constructed and analyzed in some detail. Galileon shock fronts are conjectured to exist. Finally, some interesting general relativistic effects are studied for galileons coupled minimally to gravity. Spherically symmetric galileon and metric solutions with naked curvature singularities are obtained and are shown to be separated from solutions which exhibit event horizons by a critical curve in the space of boundary data.