Self-similar static spherically symmetric scalar field models
type: Item
instance of: scholarly article
title: Self-similar static spherically symmetric scalar field models
zbMATH Open document ID: 1021.83002
DOI: 10.1023/A:1022930418343
author: Yanjing He
author: Alan Coley
published in: General Relativity and Gravitation
publication date: 2003-05-25T00:00:00Z
review text: The paper under review provides a thorough study of the class of self-similar static spherically symmetric models with two non-interacting scalar fields with exponential potentials. The global dynamics depends upon the scalar self-interaction potential parameters. After developing the governing system of evolution equations for the self-similar model under investigation, the authors introduce bounded variables in terms of the potential parameters. Then they derive the corresponding autonomous system of ordinary differential equations in terms of the new variables. Since the resulting dynamical phase space is compact, dynamical systems techniques can be applied to the analysis. By finding monotonic functions in various invariant sets and analyzing the phase spaces of the invariant sets where no monotonic functions can be found, the existence of periodic orbits or recurrent orbits in the global phase space can be ruled out. Since the existence of any heterocyclic cycles also can be ruled out, the conclusion is that the only possible asymptotic state of an orbit in the phase space is an equilibrium point. Hence the local behaviour near equilibrium points is of importance for understanding the asymptotic states of the orbits within phase space. It is interesting to see that when the solutions generically evolve away from an expanding massless scalar fields model or an expanding single scalar field model and thereafter converge towards a contracting massless scalar fields model or a contracting single scalar field model, a single scalar field model can represent the early-time or late-time asymptotic dynamical state of the self-similar models. The dynamics in the physical invariant set which constitutes part of the boundary of the five-dimensional timelike self-similar physical region are discussed in more detail.
Mathematics Subject Classification ID: 83-02
Mathematics Subject Classification ID: 83C15
Mathematics Subject Classification ID: 83F05
zbMATH DE Number: 1915854
zbMATH Keywords: self-similar
zbMATH Keywords: spherically symmetric scalar field
zbMATH Keywords: scalar fields
zbMATH Keywords: exponential potentials
zbMATH Keywords: equilibrium points
reviewed by: Walter Schempp
MaRDI profile type: Publication
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full work available at URL: a:1022930418343
OpenAlex ID: W1630275619
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description: scientific article; zbMATH DE number 1915854