Topologically massive gravity on AdS${}_2$ spacetimes

Abstract

We study the topologically massive gravity with a negative cosmological constant on AdS${}_2$ spacetimes by making use of dimensional reduction. For a constant dilaton, this two-dimensional model admits three AdS${}_2$ vacuum solutions, which are related to AdS${}_3$ and warped AdS${}_3$ with an identification upon uplifting three dimensions. We carry out the perturbation analysis around these backgrounds to find what is a physically propagating field. It turns out that a mode of $\delta F=(h-f/e)$ is merely a redundant field of dilaton $\phi$ in the absence of Chern-Simons terms, while it becomes a massive scalar in the presence of Chern-Simons terms. This shows clearly that the proper number of physically propagating degrees of freedom is one for the topologically massive gravity. Moreover, at the points of $K=l,l/3$, $\delta F$ becomes a massless scalar which implies that there is no physically propagating degrees of freedom at the chiral point.

24 pages, 3 figures, added appendix, version to appear in JHEP

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• Energy of asymptotically AdS black holes in Exotic Massive Gravity and its log-extension
• Entropy function approach to charged BTZ black hole
• Critical gravity on AdS2 spacetimes
• Nonpropagation of massive mode on AdS2 in topologically massive gravity
• Softly higher-derivative massive gravity