The Similarity Hypothesis in General Relativity

Details The Similarity Hypothesis in General Relativity The Similarity Hypothesis in General Relativity

2005-08-10

arxiv.org/abs/gr-qc/0508039v2

Gen.Rel.Grav.37:2165-2188,2005

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

to be submitted to Gen. Rel. Grav

Scientific paper

10.1007/s10714-005-0196-7

Self-similar models are important in general relativity and other fundamental theories. In this paper we shall discuss the ``similarity hypothesis'', which asserts that under a variety of physical circumstances solutions of these theories will naturally evolve to a self-similar form. We will find there is good evidence for this in the context of both spatially homogenous and inhomogeneous cosmological models, although in some cases the self-similar model is only an intermediate attractor. There are also a wide variety of situations, including critical pheneomena, in which spherically symmetric models tend towards self-similarity. However, this does not happen in all cases and it is it is important to understand the prerequisites for the conjecture.

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