The Einstein-Vlasov system in spherical symmetry II: spherical perturbations of static solutions

Abstract

We reduce the equations governing the spherically symmetric perturbations of static spherically symmetric solutions of the Einstein-Vlasov system (with either massive or massless particles) to a single stratified wave equation $-{\psi }_{,tt}=H\psi$, with $H$ containing second derivatives in radius, and integrals over energy and angular momentum. We identify an inner product with respect to which $H$ is symmetric, and use the Ritz method to approximate the lowest eigenvalues of $H$ numerically. For two representative background solutions with massless particles we find a single unstable mode with a growth rate consistent with the universal one found by Akbarian and Choptuik in nonlinear numerical time evolutions.

References in corpus (4)

• A numerical investigation of the stability of steady states and critical phenomena for the spherically symmetric Einstein-Vlasov system
• Critical collapse in the spherically-symmetric Einstein-Vlasov model
• A class of dust-like self-similar solutions of the massless Einstein-Vlasov system
• 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

Cited by in corpus (2)

• Accretion of the Vlasov gas on Reissner-Nordström black holes
• Gravitational collapse in the vicinity of the extremal black hole critical point