Abstract
Theories of massive gravity inevitably include an auxiliary reference metric. Generically, they also contain an inconsistency known as the Boulware-Deser ghost. Recently, a family of non-linear massive gravity actions, formulated with a flat reference metric, were proposed and shown to be ghost free at the complete non-linear level. In this paper we consider these non-linear massive gravity actions but now formulated with a general reference metric. We extend the proof of the absence of the Boulware-Deser ghost to this case. The analysis is carried out in the ADM formalism at the complete non-linear level. We show that in these models there always exists a Hamiltonian constraint which, with an associated secondary constraint, eliminates the ghost. This result considerably extends the range of known consistent non-linear massive gravity theories. In addition, these theories can also be used to describe a massive spin-2 field in an arbitrary, fixed gravitational background. We also discuss the positivity of the Hamiltonian.
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ArXiv ePrint: 1109.3230
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Hassan, S.F., Rosen, R.A. & Schmidt-May, A. Ghost-free massive gravity with a general reference metric. J. High Energ. Phys. 2012, 26 (2012). https://doi.org/10.1007/JHEP02(2012)026
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DOI: https://doi.org/10.1007/JHEP02(2012)026