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Critical gravity on AdS2 spacetimes · Around

2011

Critical gravity on AdS2 spacetimes

Myung, Yun Soo, Kim, Yong-Wan, Park, Young-Jai

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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.

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