The similarity hypothesis in general relativity

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 phenomena, in which spherically symmetric models tend towards self-similarity. However, this does not happen in all cases and it is important to understand the prerequisites for the conjecture.