Constraint structure of the three dimensional massive gravity

TL;DR

This paper analyzes the constraint structure of three-dimensional new massive gravity in the Palatini formalism, revealing that only two of the six metric components are dynamical, consistent with a single massive graviton.

Contribution

It provides a detailed constraint analysis of 3D massive gravity in the Palatini formalism, clarifying the dynamical degrees of freedom and their relation to the linearized theory.

Findings

Two of six metric components are dynamical.

The dynamical degrees of freedom match the linearized Fierz-Pauli theory.

The analysis confirms the existence of one massive graviton.

Abstract

Constraint analysis of the three-dimensional massive gravity, the so- called new massive gravity, is studied in the Palatini formalism. We show that amongst 6 components of the metric, 2 are dynamical, which is compatible with the existence of one vector massive graviton in the linearized theory (Fierz-Pauli theory).