Conformal Solutions of Static Plane Symmetric Cosmological Models in Cases of a Perfect Fluid and a Cosmic String Cloud

TL;DR

This paper derives exact conformal solutions for static plane symmetric cosmological models with perfect fluid and cosmic string clouds, revealing properties like dark energy behavior and asymptotic flatness, contributing to understanding exact solutions in Einstein's equations.

Contribution

It presents new exact conformal solutions for plane symmetric cosmological models with perfect fluid and cosmic strings, including their physical and geometric properties.

Findings

Solutions exhibit dark energy with negative pressure

Cosmic string densities decrease and vanish at infinity

Static solutions reduce to anti-De Sitter space

Abstract

In this work, we obtained exact solutions of Einstein's field equations for plane symmetric cosmological models by assuming that thy admit conformal motion. The space-time geometry of these solutions is found to be nonsingular, non-vacuum and conformally flat. We have shown that in the case of a perfect fluid, these solutions have an energy-momentum tensor possessing dark energy with negative pressure and the energy equation of state is $\rho +p=0$. We have shown that a fluid has acceleration, rotation, shear-free, vanishing expansion, and rotation. In the case of a cosmic string cloud, we found that the tension density and particle density decrease as the fluid moves along the direction of the strings, then vanish at infinity. We shown that the exact conformal solution for a static plane symmetric model reduces to the the well-known anti-De Sitter space time. We obtained that the space-time under consideration admits a conformal vector field orthogonal to the four-velocity vector and does not admits a vector parallel to the four-velocity vector. Some physical and kinematic properties of the resulting models are also discussed.