Bigravity in Kuchar's Hamiltonian formalism. 2. The special case

Abstract

It is proved, that, in order to avoid the ghost mode in bigravity theory, it is sufficient to impose four conditions on the potential of interaction of the two metrics. First, the potential should allow its expression as a function of components of the two metrics' 3+1 decomposition. Second, the potential must satisfy the first order linear differential equations which are necessary for the presence of four first class constraints in bigravity. Third, the potential should be a solution of the Monge-Ampere equation, where the lapse and shift are considered as variables. Fourth, the potential must have a nondegenerate Hessian in the shift variables. The proof is based on the explicit derivation of the Hamiltonian constraints, the construction of Dirac brackets on the base of a part of these constraints, and calculation of other constraints' algebra in these Dirac brackets. As a byproduct, we prove that these conditions are also sufficient in the massive gravity case.

31 pages,5 tables, references added, typos removed

References in corpus (19)

• Resummation of Massive Gravity
• Infrared-modified gravities and massive gravitons
• Acausality of Massive Gravity
• Evidence for and Obstructions to Non-Linear Partially Massless Gravity
• On Partially Massless Bimetric Gravity
• Nonlinear Partially Massless from Massive Gravity?
• Degrees of Freedom in Massive Gravity
• Higher Derivative Gravity and Conformal Gravity From Bimetric and Partially Massless Bimetric Theory
• Bimetric Theory and Partial Masslessness with Lanczos-Lovelock Terms in Arbitrary Dimensions
• Canonical structure of Tetrad Bimetric Gravity
• Chiral description of ghost-free massive gravity
• Weak Massive Gravity
• Superluminal Propagation and Acausality of Nonlinear Massive Gravity
• Aspects of Infrared Modifications of Gravity
• Bigravity in Kuchar's Hamiltonian formalism. 1. The general case
• Hamiltonian Formalism of General Bimetric Gravity
• Is Bimetric Gravity Really Ghost Free?
• Hamiltonian Formalism of Particular Bimetric Gravity Model
• Ultralocal energy density in massive gravity

Cited by in corpus (11)

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