Ghost-free Massive Gravity with a General Reference Metric

Details Ghost-free Massive Gravity with a General Reference Metric Ghost-free Massive Gravity with a General Reference Metric

2011-09-15

arxiv.org/abs/1109.3230v2

Physics

High Energy Physics

High Energy Physics - Theory

v2: references, comments and a new subsection 3.5 added, discussion of the secondary constraint updated

Scientific paper

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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