Warped AdS_3 Black Holes

TL;DR

This work shows that topologically massive gravity with negative cosmological constant admits warped AdS$_3$ vacua for all ν, including spacelike, timelike, and null variants, and highlights a critical transition at μℓ=3. For μℓ>3, known warped black holes are realized as discrete quotients of warped AdS$_3$, and the authors provide a general quotient framework that yields a family of black-hole–like spacetimes with varied causal structures. The thermodynamics of spacelike stretched warped black holes aligns with a dual 2D CFT description, enabling explicit central charges $c_L$ and $c_R$ and a Cardy-form entropy; this motivates a holographic duality conjecture for warped AdS$_3$ gravity under suitable boundary conditions. Overall, the paper extends the landscape of warped AdS$_3$ geometries, clarifies their quotient construction, and connects their thermodynamics to a proposed boundary CFT, with implications for holography beyond standard AdS$_3$/CFT$_2$.

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 μ. These are all known to be perturbatively unstable except at the recently explored chiral point μ\ell=1. However we show herein that for every value of μ\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 μ\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 μ\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 μ\ell>3, the warped AdS_3 ground state of TMG is holographically dual to a 2D boundary CFT with central charges c_R={15(μ\ell)^2+81\over Gμ((μ\ell)^2+27)} and c_L={12 μ\ell^2\over G((μ\ell)^2+27)}.