More on New Massive Gravity: Exact Solutions

Abstract

We give a novel description of the recently proposed theory of new massive gravity (NMG) in three dimensions. We show that in terms of a Dirac type differential operator acting on the traceless Ricci tensor, the field equations of the theory reduce to the massive Klein-Gordon type equation with a curvature-squared source term and to a constraint equation. Under a certain relation between the source tensor and the traceless Ricci tensor, fulfilled for constant scalar curvature, the field equations of topologically massive gravity (TMG) can be thought of as the "square-root" of the massive Klein-Gordon type equation. Using this fact, we establish a simple framework for mapping all known algebraic types D and N solutions of TMG into NMG. We also present new exact solutions of algebraic types D and N which are only inherent in NMG.

4 pages, twocolumn REVTeX; Minor cosmetic changes made and new metric added

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• Some exact solutions of all f(Ricci) theories in three dimensions
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• Holographic Renormalization and Stress Tensors in New Massive Gravity
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• On Exact Solutions and the Consistency of 3D Minimal Massive Gravity
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• Critical solutions in topologically gauged N=8 CFTs in three dimensions
• Gravity Waves in Three Dimensions
• Type N Spacetimes as Solutions of Extended New Massive Gravity
• Unitarity of Weyl-Invariant New Massive Gravity and Generation of Graviton Mass via Symmetry Breaking
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• New class of spin projection operators for 3D models
• Homogeneous Solutions of Minimal Massive 3D Gravity
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• Dynamical Black Holes in 2+1 Dimensions
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• Hamiltonian analysis of symmetries in a massive theory of gravity
• Linearized gravity in terms of differential forms
• Quadratic Curvature Gravity with Second Order Trace and Massive Gravity Models in Three Dimensions
• Solutions with pure radiation and gyratons in 3D massive gravity theories
• Some properties of the de Sitter black holes in three dimensional spacetime
• Impulsive gravitational waves in general massive 3D gravity
• Effects of curvature and gravity from flat spacetime