Hamiltonian Formalism of General Bimetric Gravity

TL;DR

This paper conducts a Hamiltonian analysis of general bimetric gravity, identifying constraints and discussing the challenges in eliminating ghost modes in non-linear cases.

Contribution

It provides a detailed Hamiltonian framework for general bimetric gravity and analyzes the nature of its constraints, highlighting difficulties in ghost mode elimination.

Findings

Identifies four first class constraints generating diagonal diffeomorphism.

Suggests remaining constraints are likely second class to maintain Hamiltonian constraint.

Highlights the difficulty of removing ghost modes in non-linear bimetric gravity.

Abstract

We perform the Hamiltonian analysis of general bimetric gravity. We determine four first class constraints that are generators of the diagonal diffeomorphism. We further analyze the remaining constraints and we present an evidence that these constraints should be the second class constraints in order to have theory with the Hamiltonian constraint as the first class constraint. We also discuss the case of the non-linear bimetric gravity and argue that it is very difficult to eliminate the ghost mode.