Analysis of constraints and their algebra in bimetric theory

Abstract

We perform a canonical analysis of the bimetric theory in the metric formulation, computing the constraints and their algebra explicitly. In particular, we compute a secondary constraint, that has been argued to exist earlier, and show that it has the correct form to eliminate the ghost. We also identify a set of four first class constraints that generate the algebra of general covariance. The covariance algebra naturally determines a spacetime metric for the theory. However, in bimetric theory, this metric is not unique but depends on how the first class constraints are identified.

arXiv comment36 pages; v2: minor improvements, reference added

References in corpus (25)

• The Dynamics of General Relativity
• Resummation of Massive Gravity
• Bimetric Gravity from Ghost-free Massive Gravity
• Resolving the Ghost Problem in non-Linear Massive Gravity
• Confirmation of the Secondary Constraint and Absence of Ghost in Massive Gravity and Bimetric Gravity
• Ghost-free Massive Gravity with a General Reference Metric
• On Non-Linear Actions for Massive Gravity
• Ghosts in Massive Gravity
• Beyond Amplitudes' Positivity and the Fate of Massive Gravity
• Proof of Consistency of Nonlinear Massive Gravity in the Stuckelberg Formulation
• On Consistent Theories of Massive Spin-2 Fields Coupled to Gravity
• Covariant constraints in ghost free massive gravity
• Massive Spin-2 Scattering and Asymptotic Superluminality
• Massive gravity: a General Analysis
• Massive and Massless Spin-2 Scattering and Asymptotic Superluminality
• On the local structure of spacetime in ghost-free bimetric theory and massive gravity
• Canonical structure of Tetrad Bimetric Gravity
• An Analysis of Characteristics in Non-Linear Massive Gravity
• Covariant Approach to the No-ghost Theorem in Massive Gravity
• Chiral description of ghost-free massive gravity
• Bigravity in Kuchar's Hamiltonian formalism. 1. The general case
• Bigravity in Kuchar's Hamiltonian formalism. 2. The special case
• Hamiltonian Formalism of Bimetric Gravity In Vierbein Formulation
• Is Bimetric Gravity Really Ghost Free?
• Hamiltonian Formalism of General Bimetric Gravity

Cited by in corpus (17)

• Combining cosmological and local bounds on bimetric theory
• Geometric mean of bimetric spacetimes
• Interactions of multiple spin-2 fields beyond pairwise couplings
• Causal propagation of constraints in bimetric relativity in standard 3+1 form
• Spherical dust collapse in bimetric relativity: Bimetric polytropes
• $\mathtt{bimEX}$: A Mathematica package for exact computations in $3+1$ bimetric relativity
• On the ratio of lapses in bimetric relativity
• Covariant BSSN formulation in bimetric relativity
• Algebraic Properties of Einstein Solutions in Ghost-Free Bimetric Theory
• Teleparallel bigravity
• The mean gauges in bimetric relativity
• On the absence of ghosts in quadratic bigravity
• Hamiltonian structure of bi-gravity, problem of ghost and bifurcation
• Constraint Algebra in Bigravity
• Mass spectrum and linear perturbations of ghost-free multi-spin-2 theory
• Symplectic realization of two interacting spin-two fields in three dimensions
• The Canonical Structure of Bigravity