Critical Collapse of Collisionless Matter in Spherical Symmetry

TL;DR

This paper presents a numerical study of the critical gravitational collapse of collisionless matter in spherical symmetry, revealing Type I behavior and scaling laws for critical solutions using a particle-mesh method.

Contribution

It introduces a particle-mesh numerical approach to simulate collisionless matter collapse and investigates the critical phenomena, showing evidence of static critical solutions with non-zero radial momentum.

Findings

Critical behavior appears to be of Type I with finite mass black holes.

Critical solutions are static spacetimes with non-zero radial momentum.

Scaling laws for the duration of the critical regime are observed.

Abstract

We perform a numerical study of the critical regime for the general relativistic collapse of collisionless matter in spherical symmetry. The evolution of the matter is given by the Vlasov equation (or Boltzmann equation) and the geometry by Einstein's equations. This system of coupled differential equations is solved using a particle-mesh (PM) method. This method approximates the distribution function which describes the matter in phase space with a set of particles moving along the characteristics of the Vlasov equation. The individual particles are allowed to have angular momentum different from zero but the total angular momentum has to be zero to retain spherical symmetry. In accord wih previous work by Rein, Rendall and Schaeffer, our results give some indications that the critical behaviour in this model is of Type I (the smallest black hole in each family has a finite mass). For the families of initial data that we have studied it seems that in the critical regime the solution is a static spacetime with non-zero radial momentum for the individual particles. We have also found evidence for scaling laws for the time that the critical solutions spend in the critical regime.