Kinematic Self-Similar Plane Symmetric Solutions

Abstract

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.

29 pages, accepted for publication in Classical Quantum Gravity

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Cited by in corpus (5)

• Plane Symmetric Solutions in f(R) Gravity
• High-Speed Cylindrical Collapse of Two Perfect Fluids
• Killing and Noether Symmetries of Plane Symmetric Spacetime
• Homotheties of a Class of Spherically Symmetric Space-Times Admitting $G_3$ as Maximal Isometry Group
• Asymptotic evolution of bulk-viscous, spherically symmetric spacetimes