Symmetrically reduced Galileon equations and solutions

TL;DR

This paper demonstrates how symmetry reductions simplify complex Galileon equations to well-understood forms, enabling explicit solutions for spherical and axial configurations.

Contribution

It introduces symmetry-based reduction techniques for Galileon equations, making them more tractable and allowing explicit solutions in symmetric cases.

Findings

Symmetry reductions simplify Galileon equations to Monge-Ampere and cubic equations.

Explicit solutions for spherical and axial symmetric Galileon fields are obtained.

Connections between reduced solutions and known implicit solutions are established.

Abstract

The maximally complicated arbitrary-dimensional "maximal" Galileon field equations simplify dramatically for symmetric configurations. Thus, spherical symmetry reduces the equations from the D- to the two-dimensional Monge-Ampere equation, axial symmetry to its cubic extension etc. We can then obtain explicit solutions, such as spherical or axial waves, and relate them to the (known) general, but highly implicit, lower-D solutions.