A numerical investigation of the steady states of the spherically symmetric Einstein-Vlasov-Maxwell system

Abstract

We construct, by numerical means, static solutions of the spherically symmetric Einstein-Vlasov-Maxwell system and investigate various features of the solutions. This extends a previous investigation \cite{AR1} of the chargeless case. We study the possible shapes of the energy density profile as a function of the area radius when the electric charge of an individual particle is varied as a parameter. We find profiles which are multi-peaked, where the peaks are separated either by vacuum or a thin atmosphere, and we find that for a sufficiently large charge parameter there are no physically meaningful solutions. Furthermore, we investigate if the inequality \sqrt{M}\leq \frac{\sqrt{R}}{3}+\sqrt{\frac{R}{9}+\frac{Q^2}{3R}}, derived in \cite{An2}, is sharp within the class of solutions to the Einstein-Vlasov-Maxwell system. Here M is the ADM mass, Q the charge, and R the area radius of the boundary of the static object. We find two classes of solutions with this property, while there is only one in the chargeless case. In particular we find numerical evidence for the existence of arbitrarily thin shell solutions to the Einstein-Vlasov-Maxwell system. Finally, we consider one parameter families of steady states, and we find spirals in the mass-radius diagram for all examples of the microscopic equation of state which we consider.

25 pages, 16 figures

References in corpus (6)

• Sharp bounds on the critical stability radius for relativistic charged spheres
• Sharp bounds on $2m/r$ of general spherically symmetric static objects
• On the steady states of the spherically symmetric Einstein-Vlasov system
• Sharp bounds on 2m/r for static spherical objects
• On static shells and the Buchdahl inequality for the spherically symmetric Einstein-Vlasov system
• Absolute Stability Limit for Relativistic Charged Spheres

Cited by in corpus (10)

• The Einstein-Vlasov System/Kinetic Theory
• An introduction to the relativistic kinetic theory on curved spacetimes
• Bounds on M/R for Charged Objects with positive Cosmological constant
• Buchdahl compactness limit and gravitational field energy
• Bounds on M/R for static objects with a positive cosmological constant
• A numerical stability analysis for the Einstein-Vlasov system
• All fundamental electrically charged thin shells in general relativity: From star shells to tension shell black holes and regular black holes and beyond
• Stable cosmologies with collisionless charged matter
• Rotating Clouds of Charged Vlasov Matter in General Relativity
• Gravitational collapse in the vicinity of the extremal black hole critical point