Ghost-free Massive Gravity with a General Reference Metric
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.
Cite
@article{arxiv.1109.3230,
title = {Ghost-free Massive Gravity with a General Reference Metric},
author = {S. F. Hassan and Rachel A. Rosen and Angnis Schmidt-May},
journal= {arXiv preprint arXiv:1109.3230},
year = {2015}
}
Comments
v2: references, comments and a new subsection 3.5 added, discussion of the secondary constraint updated