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Existence of Axially Symmetric Static Solutions of the Einstein-Vlasov System

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Abstract

We prove the existence of static, asymptotically flat non-vacuum spacetimes with axial symmetry where the matter is modeled as a collisionless gas. The axially symmetric solutions of the resulting Einstein-Vlasov system are obtained via the implicit function theorem by perturbing off a suitable spherically symmetric steady state of the Vlasov-Poisson system.

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Authors and Affiliations

  1. Mathematical Sciences, Chalmers University of Technology, Göteborg University, 41296, Göteborg, Sweden

    Håkan Andréasson

  2. Fakultät für Mathematik, Universität Duisburg-Essen, 45117, Essen, Germany

    Markus Kunze

  3. Fakultät für Mathematik, Physik und Informatik, Universität Bayreuth, 95440, Bayreuth, Germany

    Gerhard Rein

Authors
  1. Håkan Andréasson
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  2. Markus Kunze
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  3. Gerhard Rein
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Correspondence to Gerhard Rein.

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Communicated by P.T. Chruściel

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Andréasson, H., Kunze, M. & Rein, G. Existence of Axially Symmetric Static Solutions of the Einstein-Vlasov System. Commun. Math. Phys. 308, 23–47 (2011). https://doi.org/10.1007/s00220-011-1324-8

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  • DOI: https://doi.org/10.1007/s00220-011-1324-8

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