The general homothetic equations

TL;DR

This paper extends the homothetic equations framework from vacuum to non-vacuum spacetimes, introduces additional integrability conditions, and applies the method to Petrov type O pure radiation solutions, broadening its applicability.

Contribution

It generalizes previous homothetic equations to include non-vacuum solutions and derives new integrability conditions, enhancing the method's scope.

Findings

Derived homothetic equations for non-vacuum spacetimes.

Provided second integrability conditions for these equations.

Applied the framework to Petrov type O pure radiation solutions.

Abstract

In an earlier paper [6] the author wrote the homothetic equations for vacuum solutions in a first order formalism allowing for arbitrary alignment of the dyad. This paper generalises that method to homothetic equations in non-vacuum spaces and also provides useful second integrability conditions. An application to the well-known Petrov type O pure radiation solutions is given.