Note About Hamiltonian Structure of Non-Linear Massive Gravity

TL;DR

This paper analyzes the Hamiltonian structure of non-linear massive gravity and finds that it has an odd number of second class constraints, indicating the presence of non-eliminable non-physical degrees of freedom.

Contribution

It provides a detailed Hamiltonian analysis of a recent non-linear massive gravity model, revealing its constraint structure and implications for degrees of freedom.

Findings

Hamiltonian constraint is second class

Theory has an odd number of second class constraints

Non-physical degrees of freedom cannot be eliminated

Abstract

We perform the Hamiltonian analysis of non-linear massive gravity action studied recently in arXiv:1106.3344 [hep-th]. We show that the Hamiltonian constraint is the second class constraint. As a result the theory possesses an odd number of the second class constraints and hence all non physical degrees of freedom cannot be eliminated.