Spherical and nonspherical models of primordial black hole formation: exact solutions

Understand

We construct spacetimes which provide spherical and nonspherical models of black hole formation in the flat Friedmann--Lemaitre--Robertson--Walker (FLRW) universe with the Lemaitre--Tolman--Bondi solution and the Szekeres quasispherical solution, respectively.

• These dust solutions may contain both shell-crossing and shell-focusing naked singularities.
• These singularities can be physically regarded as the breakdown of dust description, where strong pressure gradient force plays a role.
• We adopt the simultaneous big bang condition to extract a growing mode of adiabatic perturbation in the flat FLRW universe.