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)…


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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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, augmented and virtual reality, and applications in biomedicine, general relativity, architecture, and geoinformation; in particular the combination of modeling, simulation and visualization to create Digital Twins of physical systems. Logg is Director of the Digital Twin Cities Centre at Chalmers, a Vinnova Competence Centre devoted to the study and development of the Digital Twin concept for city modeling and simulation. Logg is co-founder and initial developer of the FEniCS Project, a leading open-source software for automated solution of PDE. He works part-time as scientific advisor to Fraunhofer-Chalmers Centre.

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