On Physical Properties of Cylindrically Symmetric Self-Similar Solutions

TL;DR

This paper analyzes the physical and kinematic properties of cylindrically symmetric self-similar solutions of the first kind, focusing on quantities like acceleration, shear, and singularity features in both co-moving and non-co-moving frames.

Contribution

It provides a detailed evaluation of kinematic quantities and singularity features of cylindrically symmetric self-similar solutions, enhancing understanding of their physical characteristics.

Findings

Evaluation of acceleration, rotation, and shear in different coordinate systems

Discussion of singularity features of the solutions

Insights into the physical behavior of self-similar solutions

Abstract

This paper is devoted to discuss some of the features of self-similar solutions of the first kind. We consider the cylindrically symmetric solutions with different homotheties. We are interested in evaluating the quantities acceleration, rotation, expansion, shear, shear invariant and expansion rate. These kinematical quantities are discussed both in co-moving as well as in non-co-moving coordinates (only in radial direction). Finally, we would discuss the singularity feature of these solutions. It is expected that these properties would help in exploring some interesting features of the self-similar solutions.