On the Physical Properties of the Plane Symmetric Self-Similar Solution

TL;DR

This paper analyzes the physical properties of plane symmetric self-similar solutions, including expansion, shear, and singularity structure, providing insights into their geometric and physical characteristics in different coordinate systems.

Contribution

It offers a detailed examination of physical and geometric properties of homothetic solutions, highlighting their singularity structure and behavior in co-moving and non-co-moving frames.

Findings

Calculation of expansion, shear, and rotation in different coordinates

Identification of singularity structures in self-similar solutions

Insights into the physical behavior of plane symmetric homothetic solutions

Abstract

This paper discusses some of the physical properties of plane symmetric self-similar solutions of the first kind (i.e., homothetic solutions). We are interested in calculating the expansion, the acceleration, the rotation, the shear tensor, the shear invariant, and the expansion rate (given by Raychaudhuri's equation). We check these properties both in co-moving and non-co-moving coordinates (only in the radial direction). Further, the singularity structure of such solutions will be explored. This analysis provides some interesting features of self-similar solutions.