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On the Physical Properties of the Plane Symmetric Self-Similar Solution
Muhammad Sharif,Sehar Aziz 한국물리학회 2005 THE JOURNAL OF THE KOREAN PHYSICAL SOCIETY Vol.47 No.3
This paper discusses some of the physical properties of plane symmetric self-similar solutions of the first kind (i.e., homothetic solutions). We are interested in calculating the expansion, the acceleration, the rotation, the shear tensor, the shear invariant, and the expansion rate (given by Raychaudhuri’s equation). We check these properties both in co-moving and non-co-moving coordinates (only in the radial direction). Further, the singularity structure of such solutions will be explored. This analysis provides some interesting features of self-similar solutions.
A Classification of Plane Symmetric Kinematic Self-Similar Solutions
M. Sharif,Sehar Aziz 한국물리학회 2006 THE JOURNAL OF THE KOREAN PHYSICAL SOCIETY Vol.49 No.1
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 of the first, second, zeroth, and infinite kinds for the tilted, orthogonal, and parallel cases have been explored with different equations of state. We obtain a total of eleven plane symmetric kinematic self-similar solutions out of which six are independent. The perfect-fluid case gives two solutions: infinite tilted and infinite orthogonal kinds of self-similarity. In the dust case, we have four independent solutions: first orthogonal, infinite tilted, infinite orthogonal, and infinite parallel kinds of self-similarity. The remaining cases are not consistent. It is interesting to mention that some of these solutions turn out to be vacuum.
Addendum: A Classification of Plane Symmetric Kinematic Self-Similar Solutions
M. Sharif,Sehar Aziz 한국물리학회 2007 THE JOURNAL OF THE KOREAN PHYSICAL SOCIETY Vol.50 No.4
In our recent paper, we classified plane symmetric kinematic self-similar perfect fluid and dust solutions of the second, zeroth and infinite kinds. However, we missed some solutions during the process. In this short communication, we add up those missing solutions. We have found a total of seven solutions, out of which five turn out to be independent and cannot be found in the earlier paper.