Collisionless equilibria in general relativity: stable configurations beyond the first binding energy maximum

TL;DR

This study numerically investigates the stability of collisionless equilibria in general relativity, challenging the binding energy hypothesis and revealing multiple stability changes in certain models.

Contribution

It provides the first numerical evidence of multiple stability changes and refutes the binding energy hypothesis in the context of Einstein-Vlasov systems.

Findings

Strong evidence against the binding energy hypothesis.

Confirmation that steady states are stable up to the first local maximum.

Observation of multiple stability changes in certain models.

Abstract

We numerically study the stability of collisionless equilibria in the context of general relativity. More precisely, we consider the spherically symmetric, asymptotically flat Einstein-Vlasov system in Schwarzschild and in maximal areal coordinates. Our results provide strong evidence against the well-known binding energy hypothesis which states that the first local maximum of the binding energy along a sequence of isotropic steady states signals the onset of instability. We do however confirm the conjecture that steady states are stable at least up to the first local maximum of the binding energy. For the first time, we observe multiple stability changes for certain models. The equations of state used are piecewise linear functions of the particle energy and provide a rich variety of different equilibria.