Stationary solutions of the axially symmetric Einstein-Vlasov system: present status and open problems
Review article, 2024

The purpose of this work is to review the status about stationary solutions of the axially symmetric Einstein-Vlasov system with a focus on open problems of both analytical and numerical nature. For the latter we emphasize that the code used to construct stationary solutions in Ames et al (2016 Class. Quantum Grav. 33 155008; 2019 Phys. Rev. D 99 024012) is open source, see Ames and Logg (2023 J. Open Source Softw. 8 5979). In the analytical setting the open problems include establishing methods for proving existence of axisymmetric stationary solutions which are far from spherically symmetric, both in the general case and for certain special classes of solutions pointed out in the text. In the numerical setting there are intriguing properties of highly relativistic solutions that demand further attention, such as whether a sequence of such stationary solutions can approach a Kerr black hole, or if they necessarily approach the thin ring limit reminiscent of cosmic strings. The question of whether stationary solutions include states with thin-disk like morphologies as seen in many galaxies is also open. Finally, there are opportunities to extend this research to new settings such as the case of massless particles and coupled black hole-matter systems. We believe that some of the open problems highlighted here are of central importance for the understanding of nature.

Einstein-Vlasov

stationary solutions

relativity

Author

Ellery Ames

Mathematics

California State Polytechnic University

Håkan Andreasson

Chalmers, Mathematical Sciences, Analysis and Probability Theory

Classical and Quantum Gravity

0264-9381 (ISSN) 13616382 (eISSN)

Vol. 41 7 073001

Subject Categories

Computational Mathematics

DOI

10.1088/1361-6382/ad29e7

More information

Latest update

3/18/2024