A Classification of Plane Symmetric Kinematic Self-Similar Solutions

TL;DR

This paper classifies plane symmetric kinematic self-similar solutions for perfect fluids and dust, identifying eleven solutions across various cases, including some that are vacuum, enhancing understanding of self-similarity in symmetric spacetimes.

Contribution

It provides a comprehensive classification of self-similar solutions in plane symmetric spacetimes, exploring different types and equations of state, and identifying new solutions including vacuum cases.

Findings

Eleven total solutions identified, six are independent.

Two solutions for perfect fluid in infinite tilted and orthogonal cases.

Four independent dust solutions in specific cases.

Abstract

In this paper we provide a classification of plane symmetric kinematic self-similar perfect fluid and dust solutions. In the perfect fluid and dust cases, kinematic self-similar vectors for the tilted, orthogonal and parallel cases have been explored in the first, second, zeroth and infinite kinds with different equations of state. We obtain total of eleven plane symmetric kinematic self-similar solutions out of which six are independent. The perfect fluid case gives two solutions for infinite tilted and infinite orthogonal kinds. In the dust case, we have four independent solutions in the first orthogonal, infinite tilted, infinite orthogonal and infinite parallel kinds. The remaining cases provide contradiction. It is interesting to mention that some of these solutions turn out to be vacuum.