Consistent massive graviton on arbitrary backgrounds

Abstract

We obtain the fully covariant linearized field equations for the metric perturbation in the de Rham-Gabadadze-Tolley (dRGT) ghost free massive gravities. For a subset of these theories, we show that the non dynamical metric that appears in the dRGT setup can be completely eliminated leading to the theory of a massive graviton moving in a single metric. This has a mass term which contains non trivial contributions of the space-time curvature. We show further how 5 covariant constraints can be obtained including one which leads to the tracelessness of the graviton on flat space-time and removes the Boulware-Deser ghost. The 5 constraints are obtained for a background metric which is arbitrary, i.e. which does not have to obey the background field equations.

Latex, 5 pages. Matches published version

References in corpus (23)

• Resummation of Massive Gravity
• Generalization of the Fierz-Pauli Action
• Massive Gravity
• Theoretical Aspects of Massive Gravity
• Bimetric Gravity from Ghost-free Massive Gravity
• Resolving the Ghost Problem in non-Linear Massive Gravity
• Confirmation of the Secondary Constraint and Absence of Ghost in Massive Gravity and Bimetric Gravity
• Ghost-free Massive Gravity with a General Reference Metric
• Interacting Spin-2 Fields
• Ghost free Massive Gravity in the Stückelberg language
• xPerm: fast index canonicalization for tensor computer algebra
• Proof of Consistency of Nonlinear Massive Gravity in the Stuckelberg Formulation
• No Van Dam-Veltman-Zakharov Discontinuity in Ads Space
• Equations of Motion for Massive Spin 2 Field Coupled to Gravity
• A note on "symmetric" vielbeins in bimetric, massive, perturbative and non perturbative gravities
• Causality of Massive Spin 2 Field in External Gravity
• Covariant constraints in ghost free massive gravity
• Tree-Level Unitarity Constraints on the Gravitational Couplings of Higher-Spin Massive Fields
• On horizon structure of bimetric spacetimes
• Note on Massive Spin 2 in Curved Space
• The Boulware-Deser mode in Zwei-Dreibein gravity
• Non linear Fierz-Pauli theory from torsion and bigravity
• Perturbations for massive gravity theories

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