Abstract
The relationship between the existence of self-similar asymptotic solutions of Einstein’s equations and equations of state is investigated. For instance, imperfect fluid Bianchi models with ‘dimensionless’ equations of state are shown to have self-similar asymptotic solutions. Conversely, it is also shown that if the spacetime is self-similar, then the resulting equations of state must be of this same ‘dimensionless’ form. The conditions under which solutions are asymptotically self-similar are discussed, and it is noted that this is not a generic property of Einstein’s equations.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Wainwright, J. and Hsu L., 1989, Class. Quantum Grav., 6, 1409.
Hewitt C.G., and Wainwright J., 1993, Class. Quantum Grav., 10, 99.
Hewitt C.G. and Wainwright J., 1990, Class. Quantum Grav., 7, 2295.
Coley A.A. and van den Hoogen R.J., 1994, submitted to J. Math. Phys.
Ellis G.F.R. and MacCallum M.A.H., 1969, Commun. Math. Phys., 12, 108.
Hsu L. and Wainwright J., 1986, Class. Quantum Grav., 3, 1105.
MacCallum M.A.H., 1973, Cargèse Lectures in Physics, vol 6, ed E. Schatzman (New York: Gordon and Breach), p 61.
Coley A.A. and Tupper B.O.J., 1990, Class. Quantum Grav., 7, 1961.
Bluman G.W. and Kumei S., 1989, Symmetries and Differential Equations (New York: Springer-Verlag).
Coley A.A., 1990, J. Math. Phys., 31, 1698.
Steinhardt P.J., 1991, Proceedings of the Sixth Marcel Grossman Meeting on General Relativity, ed H. Sato and T. Nakamura (Singapore: World Scientific), p 269.
King A.R. and Ellis G.F.R., 1973, Commun. Math. Phys., 31, 209.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1994 Springer Science+Business Media New York
About this chapter
Cite this chapter
Coley, A.A., van den Hoogen, R.J. (1994). Self-Similar Asymptotic Solutions of Einstein’s Equations. In: Hobill, D., Burd, A., Coley, A. (eds) Deterministic Chaos in General Relativity. NATO ASI Series, vol 332. Springer, Boston, MA. https://doi.org/10.1007/978-1-4757-9993-4_16
Download citation
DOI: https://doi.org/10.1007/978-1-4757-9993-4_16
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4757-9995-8
Online ISBN: 978-1-4757-9993-4
eBook Packages: Springer Book Archive