Warped AdS ₃ black holes

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 .