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

TL;DR

This paper analyzes the Hamiltonian structure of ghost-free tri- and multi-gravity theories, demonstrating the consistency of constraints that ensure the absence of ghosts and the preservation of diffeomorphism invariance.

Contribution

It provides a detailed Hamiltonian formulation of multi-gravity theories, establishing the constraint structure necessary for ghost-free and diffeomorphism-invariant models.

Findings

Constraint system structure identified for multi-gravity

Additional constraints can ensure ghost freedom

Diffeomorphism invariance maintained in Hamiltonian formalism

Abstract

We study the Hamiltonian structure of tri-gravity and four-gravity in the framework of ADM decomposition of the corresponding metrics. Hence we can deduce the general structure of the constraint system of multi-gravity. We will show it is possible and consistent to assume additional constraints which provide the needed first class constraints for generating diffeomorphism as well as enough second class constraints to omit the ghosts.