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In three dimensions, there exist modifications of Einsteins 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.
The equivalence between Chern-Simons and Einstein-Hilbert actions in three dimensions established by A.~Achucarro and P.~K.~Townsend (1986) and E.~Witten (1988) is generalized to the off-shell case. The technique is also generalized to the Yang-Mills
Three dimensional Einstein gravity with negative cosmological constant -1/ell^2 deformed by a gravitational Chern-Simons action with coefficient 1/mu is studied in an asymptotically AdS_3 spacetime. It is argued to violate unitary or positivity for g
We show that three-dimensional massive gravity admits Lifshitz metrics with generic values of the dynamical exponent z as exact solutions. At the point z=3, exact black hole solutions which are asymptotically Lifshitz arise. These spacetimes are thre
We study quantum corrections to projectable Horava gravity with $z = 2$ scaling in 2+1 dimensions. Using the background field method, we utilize a non-singular gauge to compute the anomalous dimension of the cosmological constant at one loop, in a normalization adapted to the spatial curvature term.
We present a new exact black hole solution in three dimensional Einstein gravity coupled to a single scalar field. This is one of the extended solutions of the BTZ black hole and has in fact $textrm{AdS}_3$ geometries both at the spatial infinity and