Minimal Massive Gravity: Conserved Charges, Excitations and the Chiral Gravity Limit

Abstract

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 (AdS) spacetimes. The field equation of the theory does not come from an action and hence 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 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. We also study the chiral gravity limit of MMG.

9 pages, reference added, typos corrected

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• On Solutions of Minimal Massive 3D Gravity
• On the Butterfly Effect in 3D Gravity
• Bulk and Boundary Unitary Gravity in 3D: MMG${}_2$
• Energy of asymptotically AdS black holes in Exotic Massive Gravity and its log-extension
• Circularly symmetric solutions of Minimal Massive Gravity at its merger point
• Entropy product of rotating black holes in three-dimensions