A Spin Coefficients Approach to Bianchi-I Space-Time in Einstein-Cartan Theory

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.