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

Understand

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.