Ghost free massive gravity in the Stuckelberg language

Massive gravity in 4 dimensions has been shown to be free of the Boulware-Deser (BD) ghost in the ADM language for a specific choice of mass terms. We show here how this is consistent with the Stuckelberg language beyond the decoupling limit, and how the constraint required to remove the BD ghost arises in this framework non-perturbatively, without the use of field redefinitions. We emphasize a subtlety in obtaining this constraint, that has been overlooked in previous literature. In both the ADM and Stuckelberg formalisms the vanishing of the determinant of a Hessian guarantees the absence of the BD ghost. Published by Elsevier B.V.