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

Abstract

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. If the density perturbation has a sufficiently homogeneous central region and a sufficiently sharp transition to the background FLRW universe, its central shell-focusing singularity is globally covered. If the density concentration is sufficiently large, no shell-crossing singularity appears and a black hole is formed. If the density concentration is not sufficiently large, a shell-crossing singularity appears. In this case, a large dipole moment significantly advances shell-crossing singularities and they tend to appear before the black hole formation. In contrast, a shell-crossing singularity unavoidably appears in the spherical and nonspherical evolution of cosmological voids. The present analysis is general and applicable to cosmological nonlinear structure formation described by these dust solutions.

28 pages, 5 figures, accepted for publication in Progress of Theoretical and Experimental Physics

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