标题： 关于三维最小质量引力的精确解和一致性 显示英文标题

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

摘要： 我们证明了拓扑质量引力的所有代数型-O、型-N和型-D以及一些 Kundt-型解都被其全息定义良好的变形所继承，即最近发现的最小质量引力。 这一构造为该理论提供了一大类常标量曲率解。 我们还研究了无源和物质耦合情况下的场方程的一致性。 由于MMG的场方程不是仅依赖于度规及其导数的拉格朗日量产生的，因此它缺乏适用于所有非奇异度规的Bianchi恒等式。 但结果表明，对于方程的解，Bianchi恒等式是满足的。 这是经典场方程一致性的必要条件，但不是充分条件，因为二阶张量方程容易受到双重散度的影响。 我们证明在无源情况下，方程的双重散度对于解来说为零。 在物质耦合情况下，我们证明对于理论的解，左边和右边的双重散度彼此相等。 这一构造完成了对场方程一致性的证明。 显示英文摘要

摘要： 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.