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

TL;DR

This paper numerically constructs axisymmetric, stationary solutions to Einstein--Vlasov and Vlasov--Poisson systems, revealing diverse density configurations and the first known solutions with ergoregions in the Einstein--Vlasov system.

Contribution

It introduces a numerical method to find axisymmetric stationary solutions, including novel solutions with ergoregions in the Einstein--Vlasov system.

Findings

Diverse stationary solutions with toroidal, disk-like, spindle-like, and composite densities.

Existence of solutions with non-zero angular momentum.

First solutions of Einstein--Vlasov system containing ergoregions.

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.