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arXiv · 1503.04726

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

Emel Altas·Bayram Tekin
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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.

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Emel Altas, Bayram Tekin. 2015-03-16. On Exact Solutions and the Consistency of 3D Minimal Massive Gravity. https://doi.org/10.1103/physrevd.92.025033

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