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

Abstract

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.