Symmetries of the Robinson-Trautman equation

TL;DR

This paper analyzes the symmetry properties of the Robinson-Trautman equation, classifies its symmetry algebras, and explores how these symmetries relate to known solutions, providing insights into its structure and solution space.

Contribution

It offers a detailed classification of point symmetries of the Robinson-Trautman equation and discusses symmetry reductions and their implications for solutions.

Findings

All known exact solutions are symmetric.

Classification of one- and two-dimensional symmetry algebras.

Discussion of higher-dimensional symmetries.

Abstract

We study point symmetries of the Robinson--Trautman equation. The cases of one- and two-dimensional algebras of infinitesimal symmetries are discussed in detail. The corresponding symmetry reductions of the equation are given. Higher dimensional symmetries are shortly discussed. It turns out that all known exact solutions of the Robinson--Trautman equation are symmetric.