Conformal vectors in general space-times

TL;DR

This paper extends a method for homothetic equations to conformal vectors in non-vacuum space-times, applying it to metrics with a three-parameter motion group on non-null orbits, broadening the understanding of conformal symmetries.

Contribution

It generalizes previous work to include conformal vectors in non-vacuum space-times using a first order formalism with arbitrary dyad alignment.

Findings

Derived conformal vector equations for non-vacuum space-times.

Applied the method to metrics with a three-parameter motion group.

Enhanced understanding of conformal symmetries in complex space-times.

Abstract

In an earlier paper (Class. Quantum Grav. 19 (2002) p.259) 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 conformal vectors in non-vacuum spaces. The method is applied to metrics admitting a three parameter motion group on non-null orbits.