Conserved quantities and Virasoro algebra in New massive gravity

TL;DR

This paper computes black hole entropy in new massive gravity using off-shell Noether methods, confirms the invariance of angular momentum, and explores holographic c-theorem implications.

Contribution

It introduces a novel off-shell Noether approach to entropy calculation and demonstrates angular momentum invariance in new massive gravity with scalar fields.

Findings

Reproduces horizon entropy for non-extremal BTZ black holes.

Shows invariance of angular momentum along the radial direction.

Extends invariance to scalar-coupled black holes, supporting holographic c-theorem.

Abstract

Using the {\it off-shell} Noether current and potential we compute the entropy for the AdS black holes in new massive gravity. For the non-extremal BTZ black holes by implementing the so-called stretched horizon approach we reproduce the correct expression for the horizon entropy. For the extremal case, we adopt standard formalism in the AdS/CFT correspondence and reproduce the corresponding entropy by computing the central extension term on the asymptotic boundary of the near horizon geometry. We explicitly show the invariance of the angular momentum along the radial direction for extremal as well as non-extremal BTZ black holes in our model. Furthermore, we extend this invariance for the black holes in new massive gravity coupled with a scalar field, which correspond to the holographic renormalization group flow trajectory of the dual field theory. This provides another realization for the holographic c-theorem.