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Self-gravitating stationary spherically symmetric systems in relativistic galactic dynamics

Published online by Cambridge University Press:  01 November 2007

MIKAEL FJÄLLBORG ,
J. MARK HEINZLE  and
CLAES UGGLA
MIKAEL FJÄLLBORG
Affiliation:
Department of Mathematics, University of Karlstad, S-651 88 Karlstad, and Department of Mathematics, Chalmers University of Technology, S-412 96 Göteborg, Sweden. e-mail: mikael.fjallborg@kau.se
J. MARK HEINZLE
Affiliation:
Institute for Theoretical Physics, University of Vienna, Boltzmanngasse 5, A-1090 Vienna, Austria. e-mail: mark.heinzle@univie.ac.at
CLAES UGGLA
Affiliation:
Department of Physics, University of Karlstad, S-651 88 Karlstad, Sweden. e-mail: claes.uggla@kau.se
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Abstract

We study equilibrium states in relativistic galactic dynamics which are described by stationary solutions of the Einstein–Vlasov system for collisionless matter. We recast the equations into a regular three-dimensional system of autonomous first order ordinary differential equations on a bounded state space. Based on a dynamical systems analysis we derive new theorems that guarantee that the steady state solutions have finite radii and masses.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 143 , Issue 3 , November 2007 , pp. 731 - 752
Copyright
Copyright © Cambridge Philosophical Society 2007

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References

REFERENCES

[1]Fackerell, E. D.. Relativistic stellar dynamics. Astrophys. J. 153 (1968), 643–660.Google Scholar
[2]Ipser, J. R. and horne, K. S. T. Relativistic, spherically symmetric star clusters I. Stability theory for radial perturbations. Astrophys. J. 154 (1968), 251–270.Google Scholar
[3]Ipser, J. R.. Relativistic, spherically symmetric star clusters II. Sufficient conditions for stability against radial perturbations. Astrophys. J. 158 (1969), 17–43.Google Scholar
[4]Ipser, J. R.. Relativistic, spherically symmetric star clusters III. Stability of compact isotropic models. Astrophys. J. 158 (1969), 17–43.Google Scholar
[5]Fackerell, E. D.. Relativistic, spherically symmetric star clusters IV. A sufficient condition for instability of isotropic clusters against radial perturbations. Astrophys. J. 160 (1970), 859–874.Google Scholar
[6]Fackerell, E. D.. Relativistic, spherically symmetric star clusters V. A relativistic version of Plummer's model. Astrophys. J. 165 (1971), 489–493.Google Scholar
[7]Martin–Garcia, J. M. and Gundlach, C.. Self-similar spherically symmetric solutions of the massless Einstein-Vlasov system. Phys. Rev. D65 (2002), 08402602.Google Scholar
[8]Rein, G. and Rendall, A. D.. Compact support of spherically symmetric equilibria in non-relativistic and relativistic galactic dynamics. Math. Proc. Camb. Phil. Soc. 128 (2000), 363–380.Google Scholar
[9]Misner, C. W., Thorne, K. S. and Wheeler, J. A.. Gravitation (W. H. Freeman and Company, 1973).Google Scholar
[10]Wainwright, J. and Ellis, G. F. R. (Eds.). Dynamical Systems in Cosmology (Cambridge University Press, 1997).CrossRefGoogle Scholar
[11]Heinzle, J. M., Röhr, N. and Uggla, C.. Dynamical systems approach to relativistic spherically symmetric static perfect fluid models. Class. Quantum Grav. 20 (2003), 4567–4586.Google Scholar
[12]Heinzle, J. M. and Uggla, C.. Newtonian stellar models. Ann. Phys. (NY) 308 (2003), 18–61.Google Scholar
[13]Baumgarte, T. W. and Rendall, A. D.. Regularity of spherically symmetric static solutions of the Einstein equations. Class. Quantum Grav. 10 (1993), 327–332.Google Scholar
[14]Heinzle, J. M., Rendall, A. D. and Uggla, C.. Theory of Newtonian self-gravitating stationary spherically symmetric systems. Math. Proc. Camb. Phil. Soc. 140 (2006), 177–192.Google Scholar
[15]Rendall, A. D. and Schmidt, B. G.. Existence and properties of spherically symmetric static fluid bodies with given equation of state. Class. Quantum Grav. 8 (1991), 985–1000.Google Scholar
[16]Le Blanc, V. G., Kerr, D. and Wainwright, J.. Asymptotic states of magnetic Bianchi VI0 cosmologies. Class. Quantum Grav. 12 (1995), 513–541.CrossRefGoogle Scholar