Hamiltonian analysis of BHT massive gravity

TL;DR

This paper performs a Hamiltonian analysis of BHT massive gravity with a cosmological constant, revealing the phase space structure, degrees of freedom, and conserved charges related to BTZ black holes.

Contribution

It provides a detailed Hamiltonian formulation of BHT massive gravity, identifying conditions for the phase space and deriving conserved charges and central charges in the AdS context.

Findings

Phase space dimension is 4 in a specific parameter sector.

Two physical degrees of freedom are identified.

Conserved charges for BTZ black holes are derived.

Abstract

We study the Hamiltonian structure of the Bergshoeff-Hohm-Townsend (BHT) massive gravity with a cosmological constant. In the space of coupling constants $(\Lambda_0,m^2)$, our canonical analysis reveals the special role of the condition $\Lambda_0/m^2\neq-1$. In this sector, the dimension of the physical phase space is found to be $N^*=4$, which corresponds to two Lagrangian degree of freedom. When applied to the AdS asymptotic region, the canonical approach yields the conserved charges of the BTZ black hole, and central charges of the asymptotic symmetry algebra.