Abstract
We revisit the problem of gravity coupled to a background metric ημν, looking for ghost-free interactions. It is known that elimination of the Boulware-Deser ghost is equivalent to a certain Hessian condition on the interacting potential. The resulting equation is a complicated nonlinear partial differential equation. To gain some insight, we consider the d = 3 case and provide evidence that the dRGT potential is the unique interaction between the spacetime metric and a background field ημν which is both Lorentzinvariant and ghost-free. Our approach uses only the ADM formulation of general relativity, without assuming any particular background. One may expect our results to extend to d = 4, but the explicit equation is far more involved.
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Bañados, M. A Note on the Uniqueness of the dRGT Massive Gravity Theory. The D = 3 Case. Gravit. Cosmol. 24, 321–330 (2018). https://doi.org/10.1134/S0202289318040047
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DOI: https://doi.org/10.1134/S0202289318040047