Hamiltonian formalism of Minimal Massive Gravity

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.