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

TL;DR

This paper analyzes the excitations and conserved charges of Minimal Massive Gravity (MMG) in 2+1 dimensions within asymptotically AdS spacetimes, and explores its chiral gravity limit, addressing the challenge of defining conserved charges without an action.

Contribution

It constructs conserved charges for MMG solutions despite the theory lacking an action, extending TMG and analyzing the chiral gravity limit.

Findings

Conserved charges are defined for MMG solutions using background Killing vectors.

The theory extends TMG with a healthy bulk and boundary behavior.

The chiral gravity limit of MMG is studied.

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.