Self-Similarity in General Relativity \endtitle

Details Self-Similarity in General Relativity \endtitle Self-Similarity in General Relativity \endtitle

1998-06-09

arxiv.org/abs/gr-qc/9806048v1

Class.Quant.Grav.16:R31-R71,1999

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

TeX document, 53 pages

Scientific paper

10.1088/0264-9381/16/7/201

The different kinds of self-similarity in general relativity are discussed, with special emphasis on similarity of the ``first'' kind, corresponding to spacetimes admitting a homothetic vector. We then survey the various classes of self-similar solutions to Einstein's field equations and the different mathematical approaches used in studying them. We focus mainly on spatially homogenous and spherically symmetric self-similar solutions, emphasizing their possible roles as asymptotic states for more general models. Perfect fluid spherically symmetric similarity solutions have recently been completely classified, and we discuss various astrophysical and cosmological applications of such solutions. Finally we consider more general types of self-similar models.

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