This paper is devoted to classify the most general plane symmetric spacetimes according to kinematic self-similar perfect fluid and dust solutions. We provide a classification of the kinematic self-similarity of the first, second, zeroth and infinite kinds with different equations of state, where the self-similar vector is not only tilted but also orthogonal and parallel to the fluid flow. This scheme of classification yields twenty four plane symmetric kinematic self-similar solutions. Some of these solutions turn out to be vacuum. These solutions can be matched with the already classified plane symmetric solutions under particular coordinate transformations. As a result, these reduce to sixteen independent plane symmetric kinematic self-similar solutions.

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 have 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.Recently, we presented a classification of kinematic self-similar plane symmetric spacetimes [1]. We have discussed the plane symmetric solutions that admit kinematic self-similar vectors of the second, zeroth, and infinite kinds when the perfect fluid is tilted to the fluid flow, parallel or orthogonal. However, we missed some cases that could provide more solutions. In this addendum, we present those missing solutions, which turn out to be five in number. Further, for the the self-similarity of the first kind (tilted), the two-fluid formalism does not work as the self-similar variable is ξ = x t . We shall investigate a different approach to obtain the solution in this case. The tilted perfect fluid yields four more solutions (one first-kind solution, two 2nd-kind solutions and one zeroth-kind solution), the parallel perfect fluid gives one infinite kind solution, and the orthogonal perfect fluid provides two *

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.

In this paper we classify static plane symmetric spacetimes according to their matter collineations. These have been studied for both cases when the energy-momentum tensor is non-degenerate and also when it is degenerate. It turns out that the non-degenerate case yields either four, five, six, seven or ten independent matter collineations in which four are isometries and the rest are proper. There exists three interesting cases where the energy-momentum tensor is degenerate but the group of matter collineations is finite-dimensional. The matter collineations in these cases are either four, six or ten.

This paper is devoted to discuss some of the features of self-similar solutions of the first kind. We consider the cylindrically symmetric solutions with different homotheties. We are interested in evaluating the quantities acceleration, rotation, expansion, shear, shear invariant and expansion rate. These kinematical quantities are discussed both in co-moving as well as in non-co-moving coordinates (only in radial direction). Finally, we would discuss the singularity feature of these solutions. It is expected that these properties would help in exploring some interesting features of the self-similar solutions.