On the steady states of the spherically symmetric Einstein-Vlasov system

Abstract

Using both numerical and analytical tools we study various features of static, spherically symmetric solutions of the Einstein-Vlasov system. In particular, we investigate the possible shapes of their mass-energy density and find that they can be multi-peaked, we give numerical evidence and a partial proof for the conjecture that the Buchdahl inequality ${\sup }_{r>0}2m(r)/r<8/9$, $m(r)$ the quasi-local mass, holds for all such steady states--both isotropic {\em and} anisotropic--, and we give numerical evidence and a partial proof for the conjecture that for any given microscopic equation of state--both isotropic {\em and} anisotropic--the resulting one-parameter family of static solutions generates a spiral in the radius-mass diagram.

34 pages, 18 figures, LaTex

References in corpus (2)

• A numerical investigation of the stability of steady states and critical phenomena for the spherically symmetric Einstein-Vlasov system
• A non-variational approach to nonlinear stability in stellar dynamics applied to the King model

Cited by in corpus (17)

• A numerical investigation of the stability of steady states and critical phenomena for the spherically symmetric Einstein-Vlasov system
• From Geometry to Numerics: interdisciplinary aspects in mathematical and numerical relativity
• An introduction to the relativistic kinetic theory on curved spacetimes
• Bounds on M/R for static objects with a positive cosmological constant
• Extreme $\ell$-boson stars
• Accretion of the Vlasov gas on Reissner-Nordström black holes
• Critical collapse in the spherically-symmetric Einstein-Vlasov model
• Spherically symmetric steady states of John elastic bodies in general relativity
• A numerical stability analysis for the Einstein-Vlasov system
• Stability and instability results for equilibria of a (relativistic) self-gravitating collisionless gas -- A review
• Collisionless equilibria in general relativity: stable configurations beyond the first binding energy maximum
• Newtonian and General Relativistic Models of Spherical Shells - II
• The Einstein-Vlasov system in spherical symmetry: reduction of the equations of motion and classification of single-shell static solutions, in the limit of massless particles
• Bifurcations in Bosonic Stars: chains and rings from spherical solutions
• Beyond Buchdahl's limit: bilayered stars and thin-shell configurations
• A Birman-Schwinger Principle in General Relativity: Linearly Stable Shells of Collisionless Matter Surrounding a Black Hole
• Existence of steady states of the massless Einstein-Vlasov system surrounding a Schwarzschild black hole