Kinematic Self-Similar Cylindrically Symmetric Solutions

TL;DR

This paper investigates cylindrically symmetric kinematic self-similar solutions for perfect fluids and dust, revealing specific cases where solutions exist or lead to contradictions, thus expanding understanding of such symmetries in general relativity.

Contribution

It systematically analyzes various self-similarity types and fluid orientations, identifying new solutions and contradictions in cylindrically symmetric spacetimes.

Findings

Orthogonal perfect fluid case yields a vacuum solution.

Parallel case leads to contradictions in both perfect fluid and dust.

Tilted case provides solutions for both perfect fluid and dust.

Abstract

This paper is devoted to find out cylindrically symmetric kinematic self-similar perfect fluid and dust solutions. We study the cylindrically symmetric solutions which admit kinematic self-similar vectors of second, zeroth and infinite kinds, not only for the tilted fluid case but also for the parallel and orthogonal cases. It is found that the parallel case gives contradiction both in perfect fluid and dust cases. The orthogonal perfect fluid case yields a vacuum solution while the orthogonal dust case gives contradiction. It is worth mentioning that the tilted case provides solution both for the perfect as well as dust cases.