On Axisymmetric and Stationary Solutions of the Self-Gravitating Vlasov System

Abstract

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.

24 pages

References in corpus (3)

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• On the rotation curves for axially symmetric disk solutions of the Vlasov-Poisson system
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