Kinematic Self-Similar Cylindrically Symmetric Solutions

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.

Kinematic self-similar plane symmetric solutions

“…This analysis has provided some interesting solutions. Recently, Sharif and Sehar [7] have investigated the KSS solutions for the cylindrically symmetric spacetimes. The analysis has been extensively given for the perfect fluid and dust cases with tilted, parallel and orthogonal vectors by using different equations of state.…”

Parallel and Orthogonal Cylindrically Symmetric Self-Similar Solutions

“…The metrics (49), (61), (80) and (82) do not correspond to any solution in the literature. It is interesting to mention here that the parallel case gives many solutions while there was no solution for this case when dealing with special metric [15]. The orthogonal case yields solutions only in the first kind and contradictory results in all other kinds while for the special metric [15], the infinite kind gives vacuum solution and no solution in any other kind.…”

“…In recent papers [15][16][17], Sharif and Aziz have explored the KSS solutions of a special cylindrically symmetric, special plane symmetric and the most general plane symmetric spacetimes. This analysis has been extensively given for the perfect fluid and dust cases with tilted, parallel and orthogonal vectors.…”

Homotheties of a Class of Spherically Symmetric Space-Time Admitting G3 as Maximal Isometry Group

“…Bin Farid et al [11] classified static plane symmetric spacetime according to their Ricci collineations (RCs) and their relation with isometries of the space-time. Sharif and Aziz [12,13] studied kinematic self-similar solutions of plane and cylindrically symmetric space-time for the perfect fluid and dust. Bokhari et al [14] and Saifullah and Shair-E-Yazdan [15] studied conformal motions in the context of plane symmetric static space-time.…”