Hamiltonian formalism of Minimal Massive Gravity

TL;DR

This paper develops the Hamiltonian formalism for three-dimensional Minimal Massive Gravity, deriving conserved charges, analyzing asymptotic symmetries, and confirming the consistency of black hole entropy calculations with conformal field theory predictions.

Contribution

It introduces a Hamiltonian framework for MMG, constructs boundary conditions, and computes conserved charges and asymptotic symmetries, including Virasoro algebras.

Findings

Conserved charges for BTZ black hole are derived.

Asymptotic symmetry algebra includes Virasoro algebras.

Black hole entropy matches Cardy formula predictions.

Abstract

We study the three-dimensional Minimal Massive Gravity (MMG) in the Hamiltonian formalism. Canonical expressions for the asymptotic conserved charges are derived by defining the canonical gauge generators. Specifically, the construction of asymptotic structure of MMG requires to introduce suitable boundary conditions. For instance, the application of this procedure is done for the BTZ black hole as a solution to the MMG field equations. The related conserved charges give the energy and angular momentum of the BTZ black hole. We also show that the Poisson bracket algebra of the improved canonical gauge generators produces an asymptotic gauge group which includes two separable versions of Virasoro algebras. Finally, we calculate the entropy of black hole from Cardy formula using the parameters of the boundary conformal field theory and show the result is consistent with the value obtained from Smarr one.