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On axisymmetric and stationary solutions of the self-gravitating Vlasov system

Journal article
Authors Ellery Ames
Håkan Andreasson
Anders Logg
Published in Classical and Quantum Gravity
Volume 33
Issue 15
Pages no. 155008
ISSN 0264-9381
Publication year 2016
Published at Department of Mathematical Sciences
Department of Mathematical Sciences, Mathematics
Pages no. 155008
Language en
Keywords Einstein-Vlasov, Vlasov-Poisson, axisymmetric stationary solutions, ergoregion, relativistic stellar-systems, general-relativity, spindle singularities, models, galaxies, spacetimes, stability, existence, rotation, matter, Astronomy & Astrophysics, Physics
Subject categories Astronomy, Astrophysics and Cosmology


Axisymmetric and stationary solutions are constructed to the Einstein-Vlasov and Vlasov-Poisson systems. These solutions are constructed numerically, using finite element methods and a fixed-point iteration in which the total mass is fixed at each step. A variety of axisymmetric stationary solutions are exhibited, including solutions with toroidal, disk-like, spindle-like, and composite spatial density configurations, as are solutions with non-vanishing net angular momentum. In the case of toroidal solutions, we show for the first time, solutions of the Einstein-Vlasov system which contain ergoregions.

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