Computation of the conformal algebra of 1+3 decomposable spacetimes

TL;DR

This paper presents a method to compute the conformal algebra of 1+3 decomposable spacetimes using conformal Killing vectors of the 3-space, with applications to constant curvature spaces and G"odel-type spacetimes.

Contribution

It introduces a systematic approach to derive the conformal algebra from 3-space CKVs and extends the method to non-decomposable spacetimes.

Findings

Conformal algebra of 1+3 decomposable spacetimes can be derived from 3-space CKVs.

Spaces of constant curvature always admit such conformal Killing vectors.

The method is applicable to G"odel-type and more general spacetimes.

Abstract

The conformal algebra of a 1+3 decomposable spacetime can be computed from the conformal Killing vectors (CKV) of the 3-space. It is shown that the general form of such a 3-CKV is the sum of a gradient CKV and a Killing or homothetic 3-vector. It is proved that spaces of constant curvature always admit such conformal Killing vectors. As an example, the complete conformal algebra of a G\"odel-type spacetime is computed. Finally it is shown that this method can be extended to compute the conformal algebra of more general non-decomposable spacetimes.