Addendum: A Classification of Plane Symmetric Kinematic Self-Similar Solutions

Abstract

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 *

Kinematic self-similar solutions of locally rotationally symmetric spacetimes

“…Sharif and Sehar [20] extended this work for cylindrically symmetric spacetimes for both perfect fluid and dust cases with tilted, parallel and orthogonal vector fields by using different equations of state. They also studied the physical properties of spherically [21], cylindrically [22] and plane [23] symmetric spacetimes.…”

“…Recently, Sharif and Sehar [24,25] have explored the KSS solutions of the most general plane symmetric spacetimes. Sintes [26] explored some KSS solutions of locally rotationally symmetric (LRS) spacetimes.…”

Conformal killing vectors of plane symmetric four dimensional lorentzian manifolds

“…This metric is obtained by solving EFEs and equation of motion under the assumption that the energy density  and pressure p satisfy an equation angular momentum conservation. Similarly metric (4.2) of case-II was obtained in [36] for different choices of the energy density  and pressure . p In this case we showed that the spacetime metric admit no proper CKV.…”

“…In this paper we did not solve the EFEs for any matter field but to analyze the effects of conformal geometry on a specific matter field we have taken some example metrics from literature, some of which were obtained by solving the EFEs. In case-I we have taken metric (4.1) form [36] and discussed its CKVs. This metric is obtained by solving EFEs and equation of motion under the assumption that the energy density  and pressure p satisfy an equation angular momentum conservation.…”

“…Another plane symmetric non-conformally flat metric, admitting self-similarity of second kind [36], is given by,…”