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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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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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