On the Generalized Massive Gravity in $AdS_3$

TL;DR

This paper explores a generalized massive gravity theory in $AdS_3$, revealing conditions under which the theory exhibits chirality and admits novel solutions with logarithmic asymptotic behaviors, expanding understanding of boundary conditions and solution space.

Contribution

It introduces a combined massive gravity model in $AdS_3$, analyzes its linearized excitations, and establishes new boundary conditions for solutions with logarithmic asymptotics.

Findings

The theory is chiral at a specific parameter line.

Logarithmic solutions are consistent at the chiral line.

A new log-square boundary condition is proposed and shown to be consistent.

Abstract

In this note we investigate the generalized massive gravity in asymptotically $AdS_3$ spacetime by combining the two mass terms of topological massive gravity and new massive gravity theory. We study the linearized excitations around the $AdS_3$ background and find that at a specific value of a certain combination of the two mass parameters (chiral line), one of the massive graviton solutions becomes the left moving massless mode. It is shown that the theory is chiral at this line under Brown-Henneaux boundary condition. Because of this degeneration of the gravitons the new log solution which has a logarithmic asymptotic behavior is also a solution to this gravity theory at the chiral line. The log boundary condition which was proposed to accommodate this log solution is proved to be consistent at this chiral line. The resulting theory is no longer chiral except at a special point on the chiral line, where another new solution with log-square asymptotic behavior exists. At this special point, we prove that a new kind of boundary condition called log-square boundary condition, which accommodates this new solution, can be consistent.