A numerical investigation of the stability of steady states and critical phenomena for the spherically symmetric Einstein-Vlasov system

TL;DR

This paper numerically examines the stability of steady states in the spherically symmetric Einstein-Vlasov system, confirming that binding energy maxima indicate instability and exploring implications for critical collapse and universality.

Contribution

It extends the conjecture linking binding energy maxima to instability to non-isotropic states and investigates the relevance of binding energy sign for evolution.

Findings

Binding energy maximum signals instability.

The sign of binding energy influences evolution.

Universality in critical collapse does not hold for Vlasov matter.

Abstract

The stability features of steady states of the spherically symmetric Einstein-Vlasov system are investigated numerically. We find support for the conjecture by Zeldovich and Novikov that the binding energy maximum along a steady state sequence signals the onset of instability, a conjecture which we extend to and confirm for non-isotropic states. The sign of the binding energy of a solution turns out to be relevant for its time evolution in general. We relate the stability properties to the question of universality in critical collapse and find that for Vlasov matter universality does not seem to hold.