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

I have a new preprint on arXiv: On Axisymmetric and Stationary Solutions of the Self-Gravitating Vlasov System. Together with Ellery Ames and Håkan Andreasson, I examine solutions to the Einstein-Vlasov system (Einstein equations with a kinetic matter model) under the assumption of axisymmetry. Computations were made in FEniCS (of course)…

### 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.