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 Bañados-Teitelboim-Zanelli black hole.

• Received 11 October 2018

DOI:https://doi.org/10.1103/PhysRevD.98.104021

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Published by the American Physical Society