The computation of the Conformal Killing Vectors of an 1+(n-1) decomposable metric

TL;DR

This paper generalizes a theorem for computing conformal algebra in 1+(n-1) decomposable spaces, showing CVFs as sums of gradient CVFs and Killing or homothetic vectors, with criteria for proper CVFs and an example with G"odel-type spacetime.

Contribution

It introduces a new criterion for identifying proper conformal vector fields in decomposable spacetimes and computes the complete conformal algebra for G"odel-type spacetime.

Findings

Conformal vector fields are sums of gradient CVFs and Killing or homothetic vectors.

A simple criterion to check for proper CVFs in decomposable spacetimes.

Complete conformal algebra of G"odel-type spacetime is explicitly computed.

Abstract

A generalisation of a known theorem concerning the computation of the conformal algebra in 1+(n-1) decomposable spaces is presented. It is shown that the general form of Conformal Vector Fields (CVF) is the sum of a gradient CVF and a Killing or Homothetic (n-1)-vector. A simple criterion is established which enables one to check if a 1+(n-1) decomposable spacetime admits proper CVF. As an example, the complete conformal algebra of a G\"odel-type spacetime is computed.