Bachian Gravity in Three Dimensions

Abstract

In three dimensions, there exist modifications of Einstein's gravity akin to the topologically massive gravity that describe massive gravitons about maximally symmetric backgrounds. These theories are built on the three-dimensional version of the Bach tensor (a curl of the Cotton-York tensor) and its higher derivative generalizations; and they are on-shell consistent without a Lagrangian description based on the metric tensor alone. We give a generic construction of these models, find the spectra and compute the conserved quantities for the Banados-Teitelboim-Zanelli black hole.

arXiv comment17 pages, a note added on MMG

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• The Holographic c-theorem and Infinite-dimensional Lie Algebras
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• Critical points of the Exotic Massive 3D Gravity
• Aspects of three-dimensional higher-curvature gravities