Self-Similar Solutions of a Bianchi Type-III Model with a Perfect Fluid and Cosmic String Cloud in Riemannian Geometry

Abstract

A Bianchi type-III cosmological model with self-similarity symmetry is investigated in cases with perfect fluid distribution and a cosmic string cloud. We show that this model admits a non-trivial homothetic vector field which possess non-null homothetic bivectors. This homothetic vector field is not parallel to its source vector (current vector). We discussed cases where the homothetic vector is either orthogonal or parallel to the 4-velocity of a fluid element. We solved Einstein’s field equations without making any assumptions on the geometry of space-time, only assuming that it admits self-similarity symmetry. We obtained new exact self-similar solutions for the Bianchi type-III model. We show that all obtained solutions are shear, and space-time is shear free in only the case where the homothetic vector field is parallel to the 4-velocity vector. The kinematical and physical properties of the obtained solutions are discussed.

Keywords

• homothetic vector field
• homothetic bivector vector field
• Einstein’s field equations
• self-similar solutions
• kinematical parameters
• energy condition