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The Newtonian limit of the spherically symmetric Vlasov-Einstein system

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Abstract

We prove that spherically symmetric solutions of the Vlasov-Einstein system with a fixed initial value converge to the corresponding solution of the Vlasov-Poisson system if the speed of lightc is taken as a parameter and tends to infinity. The convergence is uniform on compact time intervals with convergence rate 1/c 2. Thus the classical Vlasov-Poisson system appears as the Newtonian limit of the general relativistic Vlasov-Einstein system in a spherically symmetric setting.

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Authors and Affiliations

  1. Mathematisches Institut der Universität München, Theresienstr. 39, W-8000, München 2, Germany

    G. Rein

  2. Max-Planck-Institut für Astrophysik, Karl-Schwarzschild-Str. 1, W-8046, Garching, Germany

    A. D. Rendall

Authors
  1. G. Rein
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  2. A. D. Rendall
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Communicated by S.-T. Yau

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Rein, G., Rendall, A.D. The Newtonian limit of the spherically symmetric Vlasov-Einstein system. Commun.Math. Phys. 150, 585–591 (1992). https://doi.org/10.1007/BF02096963

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  • DOI: https://doi.org/10.1007/BF02096963

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