First Order Symmetry Operators for the Linearized Field Equation of Metric Perturbations

TL;DR

This paper characterizes the first order symmetry operators for linearized metric perturbations in higher-dimensional spacetimes, revealing a new component involving Killing-Yano 3-forms beyond coordinate invariance.

Contribution

It identifies the complete form of symmetry operators, including a novel contribution from Killing-Yano 3-forms, for the linearized field equations of metric perturbations.

Findings

Symmetry operators include coordinate invariance and Killing-Yano 3-forms.

The form of these operators is explicitly determined for D≥4.

Killing-Yano 3-forms play a role in symmetry operators for metric perturbations.

Abstract

We determine the general form of the first order linear symmetry operators for the linearized field equation of metric perturbations in the spacetimes of dimension D>=4. Apart from the part derived easily from the invariance under general coordinate transformations, we find a part consisting of a Killing-Yano 3-form.