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

References in corpus (6)

• Massive Gravity in Three Dimensions
• More on Massive 3D Gravity
• Ghost-free, finite, fourth order D=3 (alas) gravity
• Warped AdS_3 black holes in new massive gravity
• Note on New Massive Gravity in $Ad{S}_3$
• Homogeneous vacua of (generalized) new massive gravity

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• Charged Black Holes in New Massive Gravity
• Weyl-Invariant Higher Curvature Gravity Theories in n Dimensions
• Type D Solutions of 3D New Massive Gravity
• Bulk and Boundary Unitary Gravity in 3D: MMG${}_2$
• New class of spin projection operators for 3D models
• Thurston Geometries in Three-Dimensional New Massive Gravity
• Inhomogeneous metrics on complex bundles in Lovelock 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
• Impulsive gravitational waves in general massive 3D gravity
• Effects of curvature and gravity from flat spacetime