Kundt spacetimes of massive gravity in three dimensions

Abstract

We study Kundt solutions of topologically massive gravity (TMG) and the new theory of massive gravity (NMG), proposed recently in arXiv:0901.1766. For topologically massive gravity, only the CSI Kundt solutions (i.e., solutions with constant scalar polynomial curvature invariants) were found very recently in arXiv:0906.3559. We find non-CSI explicit solutions of TMG, when $\Lambda =-{\mu }^2$, and these are the first such solutions. For the new theory of massive gravity, after reducing the field equations to a manageable system of differential equations, the CSI solutions are discussed in detail, with a focus on a subfamily whose solutions are particulary easy to describe. A number of properties of Kundt solutions of TMG and NMG, such as an identification of solutions which lie at the intersection of the full non-linear and linearized theories, are also derived.

31 pages, 7 figures

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• Microscopic entropy of the three-dimensional rotating black hole of BHT massive gravity
• New Exact Solutions of Quadratic Curvature Gravity
• Gravitational solitons, hairy black holes and phase transitions in BHT massive gravity
• More on Asymptotically Anti-de Sitter Spaces in Topologically Massive Gravity
• Kundt solutions of Minimal Massive 3D Gravity
• Energy of asymptotically AdS black holes in Exotic Massive Gravity and its log-extension
• Dynamical Black Holes in 2+1 Dimensions
• Formation of Black Holes in Topologically Massive Gravity
• Solutions with pure radiation and gyratons in 3D massive gravity theories
• Asymptotically flat black holes and gravitational waves in three-dimensional massive gravity