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.

17 pages, a note added on MMG

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• More on vacua of exotic massive 3D gravity
• Unitary Extension of Exotic Massive 3D Gravity from Bi-gravity
• The Holographic c-theorem and Infinite-dimensional Lie Algebras
• Nonlocal Massive Gravity from Einstein Gravity
• On-shell versus Off-shell Equivalence in 3D Gravity
• Holographic Entanglement Entropy in $T\bar{T}$-deformed CFTs
• New canonical analysis for higher order topologically massive gravity
• A Review of Third Way Consistent Theories
• Exotic Massive Gravity: Causality and a Birkhoff-like Theorem
• Chern-Simons-Like Formulation of Exotic Massive 3D Gravity Models
• Hairy Black holes in General Minimal Massive Gravity
• Critical points of the Exotic Massive 3D Gravity
• Aspects of three-dimensional higher-curvature gravities