# Warped $$AdS_3$$ Black Holes

 Title: Warped $$AdS_3$$ Black Holes Author: Anninos, Dionysios; Li, Wei; Padi, Megha; Song, Wei; Strominger, Andrew E. Note: Order does not necessarily reflect citation order of authors. Citation: 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. Full Text & Related Files: 0807.3040v1.pdf (280.4Kb; PDF) 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 $$c_L = \frac{12\mu\ell^2}{G((\mu\ell)^2 + 27)}$$. Published Version: doi:10.1088/1126-6708/2009/03/130 Other Sources: http://arxiv.org/abs/0807.3040 Terms of Use: This article is made available under the terms and conditions applicable to Open Access Policy Articles, as set forth at http://nrs.harvard.edu/urn-3:HUL.InstRepos:dash.current.terms-of-use#OAP Citable link to this page: http://nrs.harvard.edu/urn-3:HUL.InstRepos:8123167

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Peer reviewed scholarly articles from the Faculty of Arts and Sciences of Harvard University