On Exact Solutions and the Consistency of 3D Minimal Massive Gravity

Abstract

We show that all algebraic Type-O, Type-N and Type-D and some Kundt-Type solutions of Topologically Massive Gravity are inherited by its holographically well-defined deformation, that is the recently found Minimal Massive Gravity. This construction provides a large class of constant scalar curvature solutions to the theory. We also study the consistency of the field equations both in the source-free and matter-coupled cases. Since the field equations of MMG do not come from a Lagrangian that depends on the metric and its derivatives only, it lacks the Bianchi identity valid for all non-singular metrics. But it turns out that for the solutions of the equations, Bianchi identity is satisfied. This is a necessary condition for the consistency of the classical field equations but not a sufficient one, since the the rank-two tensor equations are susceptible to double-divergence. We show that for the source-free case the double-divergence of the field equations vanish for the solutions. In the matter-coupled case, we show that the double-divergence of the left-hand side and the right-hand side are equal to each other for the solutions of the theory. This construction completes the proof of the the consistency of the field equations.

arXiv comment8 pages

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• Gravity Waves in Three Dimensions
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• New Improved Massive Gravity and Three Dimensional Spacetimes of Constant Curvature and Constant Torsion
• Homogeneous Solutions of Minimal Massive 3D Gravity
• Holographically Viable Extensions of Topologically Massive and Minimal Massive Gravity?
• Holographic Renormalization of 3D Minimal Massive Gravity
• Evanescent gravitons in Warped Anti-de Sitter space
• Exotic Massive Gravity: Causality and a Birkhoff-like Theorem
• Matter coupling in Minimal Massive 3D Gravity and spinor-matter interactions in exterior algebra formalism
• Instability of BTZ black holes in parity-even massive gravity
• Solutions with pure radiation and gyratons in 3D massive gravity theories
• Non-linear regime of the Generalized Minimal Massive Gravity in critical points
• Entropy product of rotating black holes in three-dimensions
• A note on the pp-wave solution of Minimal Massive 3D Gravity coupled with Maxwell-Chern-Simons theory