Using the Newman-Penrose-Jogia-Griffith spin coefficients approach, we obtain an exact solution for a Bianchi Type-I metric for a nonvanishing component of spin with torsion in the context of the Einstein–Cartan theory, and the solution is found to be Petrov type D. It is observed that in the absence of torsion the solution reduces to Petrov type O.

中文翻译：

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爱因斯坦-卡丹理论中比安奇-I时空的自旋系数方法

使用Newman-Penrose-Jogia-Griffith自旋系数方法，我们在爱因斯坦-卡坦理论的背景下，获得了自旋不带扭力的Bianchi I型度量的精确解，该解为彼得罗夫D型。据观察，在没有扭转的情况下，溶液还原为彼得罗夫O型。