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arXiv · 1106.0546

Critical gravity on AdS2 spacetimes

Yun Soo Myung·Yong-Wan Kim·Young-Jai Park
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Abstract

We study the critical gravity in two dimensional AdS (AdS$_2$) spacetimes, which was obtained from the cosmological topologically massive gravity (TMG$_\Lambda$) in three dimensions by using the Kaluza-Klein dimensional reduction. We perform the perturbation analysis around AdS$_2$, which may correspond to the near-horizon geometry of the extremal BTZ black hole obtained from the TMG$_\Lambda$ with identification upon uplifting three dimensions. A massive propagating scalar mode $\delta F$ satisfies the second-order differential equation away from the critical point of $K=l$, whose solution is given by the Bessel functions. On the other hand, $\delta F$ satisfies the fourth-order equation at the critical point. We exactly solve the fourth-order equation, and compare it with the log-gravity in two dimensions. Consequently, the critical gravity in two dimensions could not be described by a massless scalar $\delta F_{\rm ml}$ and its logarithmic partner $\delta F^{\rm 4th}_{\rm log}$.

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Yun Soo Myung, Yong-Wan Kim, Young-Jai Park. 2011-06-03. Critical gravity on AdS2 spacetimes. https://doi.org/10.1103/physrevd.84.064042

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