Minimal massive gravity: Conserved charges, excitations, and the chiral gravity limit

We find the excitations and construct the conserved charges (mass and angular momentum) of the recently found minimal massive gravity (MMG) in $2+1$ dimensions in asymptotically anti-de Sitter spacetimes. The field equation of the theory does not come from an action and lacks the required Bianchi identity needed to define conserved charges. But the theory, which also provides a healthy extension of the topologically massive gravity in the bulk and boundary of spacetime, does admit conserved charges for the metric that are solutions. Our construction is based on background Killing vectors and imperative to provide physical meaning to the integration constants in the black hole-type metrics. As an example, we compute the mass and angular momentum of the Bañados-Teitelboim-Zanelli black hole in MMG. We also find the central charges of the boundary field theory and study the chiral gravity limit of MMG.