On the Hamiltonian form of 3D massive gravity

TL;DR

This paper develops a Hamiltonian formulation for 3D massive gravity models, providing insights into their degrees of freedom and stability, especially highlighting issues with linearization instability in certain limits.

Contribution

It introduces a Chern-Simons-like action and derives a Hamiltonian form for the general massive gravity model in 3D, clarifying its degrees of freedom.

Findings

Number of degrees of freedom matches linearized analysis.

Linearization instability identified in specific limits.

Provides a simplified Hamiltonian framework for the model.

Abstract

We present a "Chern-Simons-like" action for the "general massive gravity" model propagating two spin-2 modes with independent masses in three spacetime dimensions (3D), and we use it to find a simple Hamiltonian form of this model. The number of local degrees of freedom, determined by the dimension of the physical phase space, agrees with a linearized analysis except in some limits, in particular that yielding "new topologically massive gravity", which therefore suffers from a linearization instability.