Stability of vacua in New Massive Gravity in different gauges

TL;DR

This paper investigates the stability of vacua in New Massive Gravity by analyzing modes in different gauges, revealing that certain massive modes have negative energy density and cannot be excluded, indicating instability.

Contribution

It provides a detailed analysis of linearized modes in various gauges for AdS3 and warped AdS3 vacua, highlighting gauge-dependent solutions and stability issues.

Findings

Massless modes in harmonic gauge have zero energy density.

All massive modes possess negative energy density.

Warped AdS3 vacuum is unstable due to non-excludable negative energy modes.

Abstract

We consider AdS3 and warped AdS3 vacua in new massive gravity and study the highest weight modes and general propagating modes as a set of solutions for the linearized equations of motion. We observed that depending on the choice of gauge there are two types of solutions. We show that for warped AdS3 vacuum, the massless modes which appear only in the harmonic gauge have zero energy density and do not get higher curvature corrections. By computing the energy density it can be shown that all massive modes have negative energy density. Our computations prove that the massive modes in warped AdS3 cannot be excluded by an appropriate boundary condition and this makes the theory unstable.