Dynamics of gravitational collapse in the axisymmetric Einstein-Vlasov system

TL;DR

This paper numerically studies the dynamics of gravitational collapse in axisymmetric Einstein-Vlasov systems, revealing critical behavior, black hole formation, and dispersal phenomena through advanced computational methods.

Contribution

It provides the first detailed numerical analysis of critical phenomena in axisymmetric Einstein-Vlasov systems, demonstrating stationary critical solutions and dispersal conditions.

Findings

Solutions exhibit type I critical behavior.

Black hole formation shows lifetime scaling.

Dispersal occurs when binding energy is nonpositive.

Abstract

We numerically investigate the dynamics near black hole formation of solutions to the Einstein--Vlasov system in axisymmetry. Our results are obtained using a particle-in-cell and finite difference code based on the $(2+1)+1$ formulation of the Einstein field equations in axisymmetry. Solutions are launched from non-stationary initial data and exhibit type I critical behaviour. In particular, we find lifetime scaling in solutions containing black holes, and support that the critical solutions are stationary. Our results contain examples of solutions that form black holes, perform damped oscillations, and appear to disperse. We prove that complete dispersal of the solution implies that it has nonpositive binding energy.