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.

Finite element variational formulation

Skärmavbild 2016-03-21 kl. 23.20.07

Selected illustrations

Skärmavbild 2016-03-21 kl. 23.20.45

 

Skärmavbild 2016-03-21 kl. 23.21.20

 

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Anders Logg is Professor of Computational Mathematics at Chalmers University of Technology. His research interests are adaptive finite element methods, high-level automating software systems for solution of PDE, domain-specific languages and compilers in scientific computing, and applications in biomedicine, general relativity, and architecture. Logg is head of the unit for Computational Mathematics and excellence profile leader within Chalmers Area of Advance the Built Environment. He is director of the Swedish Network for Mathematics in Industry and member of the EMS Applied Mathematics Committee and the Swedish National Committee for Mathematics. He is co-founder and a core developer of the FEniCS Project, a leading open-source software for automated solution of PDE. Logg works part-time as scientific advisor to Fraunhofer-Chalmers Centre and Simula Research Laboratory.

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