Massive spin-2 field in arbitrary spacetimes -- the detailed derivation

Abstract

We present the consistent theory of a free massive spin-2 field with 5 degrees of freedom propagating in spacetimes with an arbitrary geometry. We obtain this theory via linearizing the equations of the ghost-free massive gravity expressed in the tetrad formalism. The theory is parameterized by a non-symmetric rank-2 tensor whose 16 components fulfill 11 constraints implied by the equations. When restricted to Einstein spaces, the theory reproduces the standard description of massive gravitons. In generic spacetimes, the theory does not show the massless limit and always propagates five degrees of freedom, even for the vanishing mass parameter. We illustrate these features by an explicit calculation for a homogeneous and isotropic cosmological background. It turns out that the spin-2 particles are always stable if they are sufficiently massive, hence they may be a part of the Dark Mater.

arXiv comment36 pages

References in corpus (27)

• Observation of Gravitational Waves from a Binary Black Hole Merger
• Resummation of Massive Gravity
• Kerr black holes with scalar hair
• Confirmation of the Secondary Constraint and Absence of Ghost in Massive Gravity and Bimetric Gravity
• Interacting Spin-2 Fields
• Superradiant Instability and Backreaction of Massive Vector Fields around Kerr Black Holes
• Kerr black holes with Proca hair
• Graviton Mass Bounds
• Holographic Polarons, the Metal-Insulator Transition and Massive Gravity
• Massive graviton as a testable cold dark matter candidate
• Acausality of Massive Gravity
• Equations of Motion for Massive Spin 2 Field Coupled to Gravity
• Heavy spin-2 Dark Matter
• Gauge gravity duality for d-wave superconductors: prospects and challenges
• A note on "symmetric" vielbeins in bimetric, massive, perturbative and non perturbative gravities
• Massive gravitons as dark matter and gravitational waves
• Self-accelerating cosmologies and hairy black holes in ghost-free bigravity and massive gravity
• Massive Gravity Simplified: A Quadratic Action
• Condensate of Massive Graviton and Dark Matter
• Consistent massive graviton on arbitrary backgrounds
• Linear spin-2 fields in most general backgrounds
• Perturbations for massive gravity theories
• Partially Massless Graviton on Beyond Einstein Spacetimes
• Propagation peculiarities of mean field massive gravity
• Massive graviton dark matter with environment dependent mass: A natural explanation of the dark matter-baryon ratio
• Stable cosmology in chameleon bigravity
• Massive gravitons in arbitrary spacetimes

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• Thermodynamics and reentrant phase transition for logarithmic nonlinear charged black holes in massive gravity
• The Ogievetsky-Polubarinov massive gravity and the benign Boulware-Deser mode
• Generation of effective massive Spin-2 fields through spontaneous symmetry breaking of scalar field
• On two-vierbein gravity action from gauge theory of conformal group