Parallel and Orthogonal Cylindrically Symmetric Self-Similar Solutions

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.Comment: 15 pages, accepted for publication in J. Korean Physical Societ

Tilted Cylindrically Symmetric Self-Similar Solutions

“…Recently, Sharif and Aziz [16] have found the KSS solutions for a special cylindrically symmetric spacetimes. This work has been extended to investigate the KSS solutions of the general cylindrically symmetric spacetime when the fluid flow is parallel as well as orthogonal [17]. However, we have left the tilted case to deal it separately.…”

“…They have also studied the self-similar solutions for a special cylindrically symmetric spacetime [16]. Recently, self-similar solutions of the general cylindrically symmetric spacetime have been investigated [17] for the parallel and orthogonal cases. In this paper, we take the most general cylindrically symmetric spacetimes and find the KSS solutions of the first, zeroth, second and infinite kinds when the KSS vector is tilted to the fluid flow both for perfect fluid and dust cases.…”