Warped \(AdS_3\) Black Holes

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)}).