Warped AdS_3 Black Holes (0807.3040v1)

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< 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)}.

• The paper identifies warped AdS3 black holes as discrete quotients in TMG, showcasing the emergence of stretched and squashed warped AdS geometries.
• The analysis demonstrates that varying the graviton mass leads to stability transitions in AdS3, with a critical metric shift at ℓ = 3 affecting spacetime properties.
• The study links black hole thermodynamics to a holographic dual by matching CFT central charges with Bekenstein-Hawking entropy, suggesting avenues for further quantum gravity research.

Insights into Warped AdS Black Holes in 3D Topologically Massive Gravity

The paper "Warped AdS Black Holes in Three-Dimensional Topologically Massive Gravity" by Dionysios Anninos et al. offers a comprehensive analysis of three-dimensional topologically massive gravity (TMG) with a negative cosmological constant. The focus is on examining the vacuum solutions that emerge due to variations in the graviton mass, particularly in the context of warped AdS geometries.

Overview of TMG and Its Peculiarities

TMG extends Einstein's theory by including a gravitational Chern-Simons term, which introduces modifications characterized by a massive propagating degree of freedom. This theory, especially when coupled with a negative cosmological constant, provides rich dynamics worth exploring. A key realization of the paper is the identification of AdS$_3$ as an unstable background in quantum theories but unveils alternative stable regimes by varying parameters, notably the graviton mass parametrized by $\ell$.

SL(2,R) × U(1) Invariance and the Spectrum of Solutions

By analyzing the structure of vacua, the authors demonstrate that for each typical coupling configuration, two distinct warped AdS$_3$ spaces emerge, maintained by SL(2,R) × U(1) symmetry. The nature of these spaces—either stretched or squashed—is pivotal and relates directly to the spacelike, timelike, or null nature of the U(1) isometry. It is noted that the critical transition at $\ell = 3$ defines a shift from stretching to squashing effects, fundamentally altering the geometry's properties.

These warped solutions, especially beyond $\ell > 3$, are identified as fertile grounds for realizing discrete quotients applicable not only within TMG but also more broadly in gravitational theories featuring similar warped AdS configurations.

Black Hole Thermodynamics and Duality Conjecture

For $\ell > 3$, the paper unveils solutions interpreted as discrete quotients akin to the BTZ black holes but within the warped AdS context. These warped black holes, analyzed thermodynamically, support the hypothesis of a holographic dual to a boundary CFT characterized by specific central charges: $$c_R = \frac{(5\ell/8 + 3)\ell}{12 G (8\ell/27 + 3)}$$ and $c_L = \frac{(4\ell)}{8G(\ell/3 + 27)}$. These expressions underscore the significant calculational insight derived by matching the Bekenstein-Hawking entropy to a CFT entropic perspective.

Implications and Future Directions

The paper ventures to speculate that this gravitational framework could entail a broader duality, one that reconciles a consistent boundary theory arising from warped AdS boundary conditions. While these considerations furnish a plausible theoretical landscape, they highlight the necessity for verifying perturbative stability—a task whose complexity is entwined with the reduced isometry group.

Additionally, the paper's methodology suggests that extending the investigation to include non-Euclidean geometric transformations or alternate boundary considerations could yield further intriguing revelations. Specifically, leveraging string theory perspectives to decode dual aspects within broader topologically massive gravity remains an open and promising agenda.

Conclusion

In summary, the authors chart a vastly detailed exploration of warped AdS$_3$ structures within TMG, elucidating new stable vacua and their implications on black hole thermodynamics and dual theoretical constructs. This work establishes a groundwork from which both theoretical and applied advancements in gravitational studies might spring, paving pathways toward elucidating the nuanced connections between warped geometries and quantum field theories.