Hamiltonian structure of bi-gravity, problem of ghost and bifurcation

Abstract

We analyze the Hamiltonian structure of a general theory of bi-gravity where the interaction term is a scalar function of the form V (X n ) where X may be g −1 f or g −1 f . We give necessary conditions for the interaction term of such a theory to be ghost free. We give a precise constraint analysis of the bi-gravity theory of Hassan-Rosen and show that the additional constraint which omit the ghost is just one possibility at the bifurcation point. * zahra.molaei@ph.iut.ac.ir † shirzad@ipm.ir

Gauge generator for bi-gravity and multi-gravity models

“…Hence, R i and P M i are first class constraints. Assuming {C, D} = Γ, we see that physically acceptable result comes out [20] on the sector Γ = 0 of the phase space. So consistency of Γ gives…”

“…Several articles have been appeared on Hamiltonian analysis of massive gravity and bi-gravity [10]- [19]. Despite some challenges, it is finally established [20,21] that HR bi-gravity possesses seven degrees of freedom corresponding to one massive and one massless graviton (and no ghost degree of freedom).…”

“…In section 2 we will review the main features of the Hamiltonian structure of bi-gravity in ADM variables given in ref. [20]. Then we use this structure in section 3 to establish the gauge generator of diffeomorphisms.…”

Hamiltonian formalism of the ghost free Tri(-Multi)gravity theory

“…There was claims that consistency procedure of constraints leads to determining the lapse functions [6], [7], while we need enough first class constraints to generate the diffeomorphism symmetry. In our recent work [8] we showed that in the canonical investigation of the system, in the full 40 dimensional phase space, we may have two sets of four first class constraints as the generators of diffeomorphism, as well as two additional second class constraints which eliminate the ghost. However, we showed that at a critical point we meet a bifurcation problem where only one branch sounds physically acceptable.…”

“…However, a perfect Hamiltonian analysis of tri-gravity and multi-gravity, based on ADM decomposition of metric variables, has not been performed yet. This is our aim in this paper, where we try to generalize our investigations concerning bi-gravity [8] first to three and four gravity and then induce the results for multi-gravity. In order to have a complete dynamical description, we have performed our investigations in the full phase space which consists 20N phase space variables including the lapse and shift functions as physical variables.…”