First order symmetry operators for the linearized field equation of 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.

On first order symmetry operators for the field equations of differential forms

“…(Conformal) Killing-Yano forms also appear in the first order symmetry operators for the equations of motion for spinor fields (see e.g. [1][2][3][4]), Rarita-Schwinger fields [5], and the metric perturbation [6]. These facts show the importance of Killing-Yano forms.…”

“…(If S is first order and Q is higher, it is also useful, but we do not consider such possibility in this paper.) First order symmetry operators for spinors, Rarita-Schwinger fields and the metric perturbation have been considered in [1][2][3][4][5][6].…”