Cosmological Effects on Black Hole Formation

TL;DR

This paper investigates how cosmological factors influence black hole formation by analyzing domain wall collapse using the functional Schrödinger equation, deriving the Sultana-Dyer black hole mass formula, and examining horizon formation times.

Contribution

It introduces a novel approach combining quantum and semi-classical analysis of domain wall collapse in cosmological settings, deriving the black hole mass formula and horizon formation times.

Findings

Horizon formation time is infinite for an asymptotic observer.

The derived mass formula aligns with the Sultana-Dyer black hole.

Classical results are consistent across various FLRW scale factors.

Abstract

The formation of cosmological black holes is investigated using the functional Schroedinger equation as observed by an asymptotic observer, assuming a spherical domain wall collapse process. The mass formula of the Sultana-Dyer black hole is derived using Israel's domain wall mathematical framework. This is used to examine the semi-classical and quantum nature of the collapsing domain wall in the general scale of an arbitrary scale factor, while ignoring evaporation and back reaction mass losses. Particular FLRW scale factors are then explored for black hole horizon formation times, all yielding the same over-all classical result, namely that an arbitrary amount of time is required for an asymptotic observer to register the formation of this surface.