Ladder operators for Klein-Gordon equation with scalar curvature term

TL;DR

This paper develops generalized ladder operators for the Klein-Gordon equation with scalar curvature in curved spacetimes, extending previous work by identifying necessary conditions involving conformal Killing vectors.

Contribution

It introduces a new method to construct ladder operators for the Klein-Gordon equation with scalar curvature, requiring specific properties of conformal Killing vectors.

Findings

Ladder operators exist if a conformal Killing vector satisfies an additional property.

Results are consistent with previous work in maximally symmetric spacetimes.

Provides necessary and sufficient conditions for ladder operator construction.

Abstract

Recently, Cardoso, Houri and Kimura constructed generalized ladder operators for massive Klein-Gordon scalar fields in space-times with conformal symmetry. Their construction requires a closed conformal Killing vector, which is also an eigenvector of the Ricci tensor. Here, a similar procedure is used to construct generalized ladder operators for the Klein-Gordon equation with a scalar curvature term. It is proven that a ladder operator requires the existence of a conformal Killing vector, which must satisfy an additional property. This property is necessary and sufficient for the construction of a ladder operator. For maximally symmetric space-times, the results are equivalent to those of Cardoso, Houri and Kimura.