Kinematic Self-Similar Solutions of Locally Rotationally Symmetric Spacetimes

TL;DR

This paper classifies kinematic self-similar solutions in locally rotationally symmetric spacetimes, identifying seventeen solutions across different metric families and self-similarity types, with some cases leading to contradictions.

Contribution

It provides a comprehensive classification of self-similar solutions in LRS spacetimes, including new solutions and clarifying cases with contradictions.

Findings

Seventeen independent solutions found, including two vacuum solutions.

Orthogonal cases lead to contradictions in all metrics.

Some solutions reduce to known cases or are ruled out due to contradictions.

Abstract

This paper contains locally rotationally symmetric kinematic self-similar perfect fluid and dust solutions. We consider three families of metrics which admit kinematic self-similar vectors of the first, 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 orthogonal case gives contradiction both in perfect fluid and dust cases for all the three metrics while the tilted case reduces to the parallel case in both perfect fluid and dust cases for the second metric. The remaining cases give self-similar solutions of different kinds. We obtain a total of seventeen independent solutions out of which two are vacuum. The third metric yields contradiction in all the cases.