Abstract
In this paper, we obtain a homothetic vector field of a plane symmetric Bianchi type-I spacetime based on Lyra geometry. We discuss the cases when the displacement vector is function of t and when it is constant. We investigate the equation of state in both two cases. A comparison between the obtained results, using Lyra geometry, and that have obtained previously in the context of General Relativity (GR), based on Riemannian geometry, will be given.
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