  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.
