Stability of warped AdS 3 vacua of topologically massive gravity

Abstract

AdS 3 vacua of topologically massive gravity (TMG) have been shown to be perturbatively unstable for all values of the coupling constant except the chiral point μℓ = 1. We study the possibility that the warped vacua of TMG, which exist for all values of μ, are stable under linearized perturbations. In this paper, we show that spacelike warped AdS 3 vacua with Compère-Detournay boundary conditions are indeed stable in the range 3$"μℓ>3. This is precisely the range in which black hole solutions arise as discrete identifications of the warped AdS 3 vacuum. The situation somewhat resembles chiral gravity: although negative energy modes do exist, they are all excluded by the boundary conditions, and the perturbative spectrum solely consists of boundary (pure large gauge) gravitons. © 2009 SISSA.