Infinite Kinematic Self-Similarity and Perfect Fluid Spacetimes

Details Infinite Kinematic Self-Similarity and Perfect Fluid Spacetimes Infinite Kinematic Self-Similarity and Perfect Fluid Spacetimes

2001-05-02

arxiv.org/abs/gr-qc/0105007v1

Gen.Rel.Grav. 33 (2001) 1863-1896

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

38 pages, 6 figures. Accepted for publication in General Relativity & Gravitation

Scientific paper

Perfect fluid spacetimes admitting a kinematic self-similarity of infinite type are investigated. In the case of plane, spherically or hyperbolically symmetric space-times the field equations reduce to a system of autonomous ordinary differential equations. The qualitative properties of solutions of this system of equations, and in particular their asymptotic behavior, are studied. Special cases, including some of the invariant sets and the geodesic case, are examined in detail and the exact solutions are provided. The class of solutions exhibiting physical self-similarity are found to play an important role in describing the asymptotic behavior of the infinite kinematic self-similar models.

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