Parallel and Orthogonal Cylindrically Symmetric Self-Similar Solutions

TL;DR

This paper classifies and analyzes cylindrically symmetric self-similar solutions for perfect fluids and dust, identifying new solutions and their correspondence with existing literature.

Contribution

It provides a comprehensive classification of kinematic self-similar solutions in cylindrically symmetric spacetimes, including new solutions and their relation to prior work.

Findings

Parallel case yields solutions for all kinds except zeroth dust.

Orthogonal perfect fluid yields stiff fluid in first kind; dust yields vacuum.

Total of 13 solutions, 11 independent, with literature correspondence.

Abstract

In this paper, we evaluate kinematic self-similar perfect fluid and dust solutions for the most general cylindrically symmetric spacetime. We explore kinematic self-similar solutions of the first, second, zeroth and infinite kinds for parallel and orthogonal cases. It is found that the parallel case gives solutions for both perfect fluid and dust cases in all kinds except the zeroth kind of the dust case where there exists no solution. The orthogonal perfect fluid case gives stiff fluid solution only in the first kind and vacuum solution for the dust case. We obtain a total of thirteen solutions out of which eleven are independent. The correspondence of these solutions with those already available in the literature is also given.