## Abstract

Three dimensional topologically massive gravity (TMG) with a negative cosmological constant -ℓ ^{-2} and positive Newton constant G admits an AdS _{3} vacuum solution for any value of the graviton mass μ. These are all known to be perturbatively unstable except at the recently explored chiral point μℓ = 1. However we show herein that for every value of μℓ 3 there are two other (potentially stable) vacuum solutions given by SL(2,) × U(1)-invariant warped AdS _{3} geometries, with a timelike or spacelike U(1) isometry. Critical behavior occurs at μℓ = 3, where the warping transitions from a stretching to a squashing, and there are a pair of warped solutions with a null U(1) isometry. For μℓ > 3, there are known warped black hole solutions which are asymptotic to warped AdS _{3}. We show that these black holes are discrete quotients of warped AdS _{3} just as BTZ black holes are discrete quotients of ordinary AdS _{3}. Moreover new solutions of this type, relevant to any theory with warped AdS _{3} solutions, are exhibited. Finally we note that the black hole thermodynamics is consistent with the hypothesis that, for μℓ > 3, the warped AdS _{3} ground state of TMG is holographically dual to a 2D boundary CFT with central charges and .

Original language | English (US) |
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Article number | 130 |

Journal | Journal of High Energy Physics |

Volume | 2009 |

Issue number | 3 |

DOIs | |

State | Published - 2009 |

Externally published | Yes |

## Keywords

- AdS-CFT correspondence
- Black holes

## ASJC Scopus subject areas

- Nuclear and High Energy Physics

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