Classification of surface charges for a spin 2 field on a curved background solution

TL;DR

This paper proves that conserved charges for a spin 2 field in a curved background are uniquely determined by the background's Killing vector fields, clarifying the structure of conserved quantities in such gravitational settings.

Contribution

It provides an explicit proof that conserved n-2 forms for a spin 2 field are uniquely characterized by the background's Killing vectors.

Findings

Conserved forms correspond to Killing vectors of the background.

The proof applies to backgrounds solving Einstein's equations with or without cosmological constant.

Clarifies the relationship between symmetries and conserved charges in gravitational theories.

Abstract

We give an explicit proof of the result that non trivial conserved n-2 forms for a spin 2 field on a background corresponding to a solution to Einstein's equation (with or without cosmological constant) are characterized uniquely by the Killing vector fields of the background.