Black hole formation from massive scalar field collapse in the Einstein-de Sitter universe

TL;DR

This paper derives an analytical criterion for the collapse of massive scalar fields into black holes in an Einstein-de Sitter universe, aiding in understanding primordial black hole formation during early cosmological phases.

Contribution

It introduces a simple analytical condition linking initial scalar field configurations to black hole formation in an Einstein-de Sitter background, applicable to primordial black hole constraints.

Findings

Derived a collapse criterion involving size and mass scales.

Applied the criterion to primordial black hole spectrum constraints.

Provided insights into early universe black hole formation processes.

Abstract

We study the spherically symmetric collapse of a real, minimally coupled, massive scalar field in an asymptotically Einstein-de Sitter spacetime background. By means of an eikonal approximation for the field and metric functions, we obtain a simple analytical criterion---involving the physical size and mass scales (the field's inverse Compton wavelength and the spacetime gravitational mass) of the initial matter configuration---for generic (non-time-symmetric) initial data to collapse to a black hole. This analytical condition can then be used to place constraints on the initial primordial black hole spectrum, by considering spherical density perturbations that re-entered the horizon during an early matter-dominated phase that immediately followed inflation.