## Warped \(AdS_3\) Black Holes

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https://doi.org/10.1088/1126-6708/2009/03/130##### Metadata

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Anninos, Dionysios, Wei Li, Megha Padi, Wei Song, and Andrew E. Strominger. 2009. Warped \(AdS_3\) black holes. Journal of High Energy Physics 2009(3): 130.##### Abstract

Three dimensional topologically massive gravity (TMG) with a negative cosmological constant \(-\ell^{-2}\) and positive Newton constant \(G\) admits an \(AdS_3\) vacuum solution for any value of the graviton mass \(\mu\). These are all known to be perturbatively unstable except at the recently explored chiral point \(\mu\ell = 1\). However we show herein that for every value of \(\mu\ell \not= 3\) there are two other (potentially stable) vacuum solutions given by \(SL(2,\Re) \times U(1)\)-invariant warped \(AdS_3\) geometries, with a timelike or spacelike \(U(1)\) isometry. Critical behavior occurs at \(\mu\ell = 3\), 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 \(\mu\ell > 3\), 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 \(\mu\ell > 3\), the warped \(AdS_3\) ground state of TMG is holographically dual to a 2D boundary CFT with central charges \(c_R = \frac{15(\mu\ell)^2 + 81}{G\mu((\mu\ell)^2 + 27)}\) and \(c_L = \frac{12\mu\ell^2}{G((\mu\ell)^2 + 27)}\).##### Other Sources

http://arxiv.org/abs/0807.3040##### Terms of Use

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http://nrs.harvard.edu/urn-3:HUL.InstRepos:8123167

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