Ghost-free massive gravity with a general reference metric

2011/09/30 by S. F. Hassan, Rachel A. Rosen, Angnis Schmidt-May · 8 citations
Physics and Astronomy · #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #Formalism (music) #General relativity #Gravitation #Gravitational field #Hamiltonian constraint #Massive gravity #Noncommutative and Quantum Gravity Theories #Parameterized post-Newtonian formalism #f(R) gravity #hep-th

paper · pdf · doi:10.1007/jhep02(2012)026

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

arxiv created 2011/12/21 · openalex publication_date 2012/02/01 · arxiv updated 2015/05/29 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05

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.

Citations

• Massive gravity: exorcising the ghost
• Pauli–Fierz gravitons on Friedmann–Robertson–Walker background
• Product CFTs, gravitational cloning, massive gravitons and the space of gravitational duals
• On relativistic wave equations for particles of arbitrary spin in an electromagnetic field
• Resummation of Massive Gravity
• Massive and mass-less Yang-Mills and gravitational fields

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• The equivalence between Finsler and non-commutative geometries by massive gravity black hole
• Hamiltonian analysis of minimal massive gravity coupled to Galileon tadpole term