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)…
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.
Finite element variational formulation