论文标题
Kerr-Schild Tetrads和Nijenhuis张量
Kerr-Schild Tetrads and the Nijenhuis Tensor
论文作者
论文摘要
我们用平坦的时空四核和（1,1）张量$ s^λ_μ$编写Kerr-Schild四元。该张量可以被视为投影操作员，因为它将（i）（i）平坦的时空四核转换为非静电四型，反之亦然，以及（ii）Minkowski时空度量指标转换为非FLAT度量指标张量，反之亦然。 $ s^λ_μ$ tensor及其倒数是根据标准的无效矢量场$l_μ$构建的，该$l_μ$定义了一般相对性的度量张量的kerr-schild形式，并产生黑孔和非线性重力波作为真空吸尘器的溶液。我们表明，在空旷的时空中，由Kerr和Schild获得的Ricci张量消失的条件也是消失的条件，该条件是由$ S^λ_$构建的Nijenhuis张量。因此，基于nijenhuis张量的理论产生了爱因斯坦场方程的重要解决方案，即黑洞和非线性引力波。我们还表明，当前的数学框架可以轻松地接受牛顿电位的修改，这些框架可能解释了与星系旋转曲线相关的远程重力效应。
We write the Kerr-Schild tetrads in terms of the flat space-time tetrads and of a (1,1) tensor $S^λ_μ$. This tensor can be considered as a projection operator, since it transforms (i) flat space-time tetrads into non-flat tetrads, and vice-versa, and (ii) the Minkowski space-time metric tensor into a non-flat metric tensor, and vice-versa. The $S^λ_μ$ tensor and its inverse are constructed in terms of the standard null vector field $l_μ$ that defines the Kerr-Schild form of the metric tensor in general relativity, and that yields black holes and non-linear gravitational waves as solutions of the vacuum Einstein's field equations. We show that the condition for the vanishing of the Ricci tensor obtained by Kerr and Schild, in empty space-time, is also a condition for the vanishing of the Nijenhuis tensor constructed out of $S^λ_μ$. Thus, a theory based on the Nijenhuis tensor yields an important class of solutions of the Einstein's field equations, namely, black holes and non-linear gravitational waves. We also show that the present mathematical framework can easily admit modifications of the Newtonian potential that may explain the long range gravitational effects related to galaxy rotation curves.
