Kinematic Self-Similar Plane Symmetric Solutions

TL;DR

This paper classifies the most general plane symmetric spacetimes with kinematic self-similarity, identifying 24 solutions and reducing them to 16 independent solutions, including vacuum cases, for different equations of state and vector orientations.

Contribution

It provides a comprehensive classification of plane symmetric kinematic self-similar solutions, including tilted, orthogonal, and parallel vector cases, expanding the understanding of such spacetimes.

Findings

Identified 24 solutions, reduced to 16 independent solutions.

Included vacuum solutions within the classification.

Matched solutions with previously known plane symmetric solutions.

Abstract

This paper is devoted to classify the most general plane symmetric spacetimes according to kinematic self-similar perfect fluid and dust solutions. We provide a classification of the kinematic self-similarity of the first, second, zeroth and infinite kinds with different equations of state, where the self-similar vector is not only tilted but also orthogonal and parallel to the fluid flow. This scheme of classification yields twenty four plane symmetric kinematic self-similar solutions. Some of these solutions turn out to be vacuum. These solutions can be matched with the already classified plane symmetric solutions under particular coordinate transformations. As a result, these reduce to sixteen independent plane symmetric kinematic self-similar solutions.