| Summary: | 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 behaivour 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. === Science, Faculty of === Physics and Astronomy, Department of === Graduate
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