Simulation of PBH formation in a matter-dominated universe

We investigate primordial black hole (PBH) formation during an early matter-dominated era using fully nonlinear numerical relativity. The initial condition is set by a functional form of the curvature perturbation including ellipticity, which makes the configuration triaxial. Two kinds of matter descriptions are considered: dust fluid and collisionless particles. In the dust fluid description, numerical computation crashes associated with the appearance of a singularity at which the fluid density diverges, unless the singularity is hidden well inside the apparent horizon. We found that, for the dust fluid description, to observe the horizon formation before calculations crash, the initial amplitude must be larger than the previous analytic estimation by a factor of 2. On the other hand, with the particle system description, calculations do not crash, and we may observe black hole formation after subsequent evolution of the system. Then the threshold of black hole formation is significantly smaller than the previous analytic estimation by an order of magnitude.