A note on the uniqueness of the dRGT massive gravity theory

Abstract

We revisit the problem of gravity coupled to a background metric ${\eta }_{\mu \nu }$, looking for ghost free interactions. It is known that elimination of the Boulware-Desewr ghost is equivalent to a certain Hessian condition on the interacting potential. We elaborate on this equation and provide a proof that dRGT potential is the unique interaction between the spacetime metric and a background field ${\eta }_{\mu \nu }$ which is both Lorentz invariant and ghost free. Our approach is fully non-perturbative using only the ADM formulation of general relativity.

19 pages, no figures

References in corpus (4)

• Resummation of Massive Gravity
• Massive Gravity
• Degrees of Freedom in Massive Gravity
• New Branches of Massive Gravity