Warped $rm AdSsb 3$ black holes

Dionysios Anninos Harvard University Wei Li Harvard University Megha Padi Harvard University Wei Song Harvard University Andrew Strominger Harvard University

Mathematical Physics mathscidoc:1702.22036

Journal of High Energy Physics, 9, (3), 130, 2009.3
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< 3 there are two other (potentially stable) vacuum solutions given by SL(2,R)x 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={15(\mu\ell)^2+81\over G\mu((\mu\ell)^2+27)} and c_L={12 \mu\ell^2\over G((\mu\ell)^2+27)}.
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@inproceedings{dionysios2009warped,
  title={Warped $rm AdSsb 3$ black holes},
  author={Dionysios Anninos, Wei Li, Megha Padi, Wei Song, and Andrew Strominger},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170228152344704291568},
  booktitle={ Journal of High Energy Physics},
  volume={9},
  number={3},
  pages={130},
  year={2009},
}
Dionysios Anninos, Wei Li, Megha Padi, Wei Song, and Andrew Strominger. Warped $rm AdSsb 3$ black holes. 2009. Vol. 9. In Journal of High Energy Physics. pp.130. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170228152344704291568.
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