2020
DOI: 10.1088/1361-6382/ab60ba
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Rotating clouds of charged Vlasov matter in general relativity

Abstract: The existence of stationary solutions of the Einstein-Vlasov-Maxwell system which are axially symmetric but not spherically symmetric is proven by means of the implicit function theorem on Banach spaces. The proof generalises the methods of [3] where a similar result is obtained for uncharged particles. Among the solutions constructed in this article there are rotating and non-rotating ones. Static solutions exhibit an electric but no magnetic field. In the case of rotating solutions, in addition to the electr… Show more

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Cited by 8 publications
(6 citation statements)
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“…Recently, in [16,17], axisymmetric and stationary solutions of the Vlasov-Poisson and Einstein-Vlasov systems were constructed numerically, based on a variety of ansätze for the DF leading to configurations with toroidal, disk-like, spindle-like and composite structures. Axially symmetric, stationary solutions of the Einstein-Vlasov and Einstein-Vlasov-Maxwell systems with and without rotation were constructed in [18][19][20] by deforming a spherically symmetric, static solution of the Vlasov-Poisson system and using the implicit function theorem. For related astrophysical work describing tori of axisymmetric collisionless plasmas around compact objects based on a quasi-stationary approximation, see [21,22].…”
Section: Introductionmentioning
confidence: 99%
“…Recently, in [16,17], axisymmetric and stationary solutions of the Vlasov-Poisson and Einstein-Vlasov systems were constructed numerically, based on a variety of ansätze for the DF leading to configurations with toroidal, disk-like, spindle-like and composite structures. Axially symmetric, stationary solutions of the Einstein-Vlasov and Einstein-Vlasov-Maxwell systems with and without rotation were constructed in [18][19][20] by deforming a spherically symmetric, static solution of the Vlasov-Poisson system and using the implicit function theorem. For related astrophysical work describing tori of axisymmetric collisionless plasmas around compact objects based on a quasi-stationary approximation, see [21,22].…”
Section: Introductionmentioning
confidence: 99%
“…In this case the total angular momentum vanishes. This result was generalized in 2014 to the stationary, rotating case [16], and extended to the Einstein-Vlasov-Maxwell case (in which the particles have charge) in 2020 [48]. These analytic results rely on a perturbation argument with the consequence that the constructed solutions can only be guaranteed to deviate slightly from spherically symmetric solutions and to have small total angular momentum.…”
Section: Analyticmentioning
confidence: 89%
“…Allowing the particles to be charged (in addition to having mass) and interact additionally through the electromagnetic field leads to the Einstein-Vlasov-Maxwell system. This system was studied numerically in 2009 by Andréasson and coauthors [13] in the spherically symmetric setting, and in 2020 Thaller used perturbation methods to prove existence of solutions in the axisymmetric setting [48]. This result is similar to the work of [16] except that the reference solution is a charged solution of the spherically symmetric Vlasov-Poisson system, and as a result the particle charge is not restricted to be small.…”
Section: Extension To the Einstein-vlasov-maxwell Systemmentioning
confidence: 92%
“…Properties of the Einstein-Vlasov system in static and spherically symmetric cases have been intensively studied, but there are still few studies on systems with rotation [14][15][16][17][18]. Since the properties of the system may greatly change depending on the presence of angular momentum, analyses for rotating systems are important.…”
Section: Introductionmentioning
confidence: 99%