Stability of warped AdS3 vacua of topologically massive gravity

TL;DR

This paper investigates the stability of warped AdS3 vacua in topologically massive gravity, finding stability under certain boundary conditions for specific coupling ranges, which has implications for black hole solutions.

Contribution

It demonstrates the linear stability of spacelike warped AdS3 vacua in TMG for ul>3 with specific boundary conditions, extending understanding beyond the chiral point.

Findings

Warped AdS3 vacua are stable for ul>3 under certain boundary conditions.

Negative energy modes are excluded by boundary conditions, leaving only boundary gravitons.

Black hole solutions correspond to discrete identifications of stable warped AdS3 vacua.

Abstract

AdS3 vacua of topologically massive gravity (TMG) have been shown to be perturbatively unstable for all values of the coupling constant except the chiral point \mu l=1. We study the possibility that the warped vacua of TMG, which exist for all values of \mu, are stable under linearized perturbations. In this paper, we show that spacelike warped AdS3 vacua with Compere-Detournay boundary conditions are indeed stable in the range \mu l > 3. This is precisely the range in which black hole solutions arise as discrete identifications of the warped AdS3 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.