三维哥德尔型线
Gödel Type Metrics in Three Dimensions
摘要：
我们证明了在任意二维背景空间中的三维G{\”o}del型流场满足Einstein-perfect流场方程。流体速度矢量场各分量只满足一个一阶偏微分方程。然后，我们表明，相同的度量解决场方程的拓扑大规模重力的二维背景几何是一个空间的恒定负高斯曲率。本文讨论了G{\”o}del型方程求解Ricci和Cotton流动方程的可能性。当矢量场$u^μ$是Killing矢量场时，我们证明了定常G{\”o}del型解最可能的引力场方程的场方程，其中相互作用拉格朗日量是电磁场和曲率张量的任意函数.
英文摘要：
We show that the G{\" o}del type Metrics in three dimensions with arbitrary two dimensional background space satisfy the Einstein-perfect fluid field equations. There exists only one first order partial differential equation satisfied by the components of fluid's velocity vector field. We then show that the same metrics solve the field equations of the topologically massive gravity where the two dimensional background geometry is a space of constant negative Gaussian curvature. We discuss the possibility that the G{\" o}del Type Metrics to solve the Ricci and Cotton flow equations. When the vector field $u^μ$ is a Killing vector field we finally show that the stationary G{\" o}del Type Metrics solve the field equations of the most possible gravitational field equations where the interaction lagrangian is an arbitrary function of the electromagnetic field and the curvature tensors.
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