A non-rotating black hole (if such exists) has a spherical accretion shell, as opposed to a wide disc. Would I be correct in assuming that this shell must be relatively thin?
Isotropic symmetry in the Schwarzschild model implies planar orbits, whereas broken symmetry of Kerr model implies vertical oscillations relative to the equatorial plane. While a shell is possible, I think it would depend a lot on initial conditions, whether or not the mass is drawn in from a surrounding cloud, or from a non-concentric, nearby cloud. Thickness is a statistical variable, so I would expect a wide range of possibilities, strongly depending on initial conditions.
A "factor" is a ratio, of what exactly? How can it be compared distance?
The ratio is apparent in the exponent of Planck's blackbody spectrum, where wavelength multiplies temperature. A covariant change of both can leave the function invariant. This implies a linear relationship between redshift and temperature. Redshift is a more common time parameter in astronomy.
From RCS: I thought the use of temp or density as a time proxy is interesting. But don't you require averages over some zone of space, which brings in issues of simultaneity?
The issue of simultaneity is already apparent in the NASA timeline image, where the CMB is depicted as planar, and that is sort-of a fraud. There is a 0.02% temperature anisotropy in the CMB, which can be interpreted as a different redshift along every line of sight. Instrument precision limits how many pixels or lines of sight we have. It's not that different from other image data, values per pixel are implicitly average values. The situation of a campfire burning out is much worse with regard to fluctuations than the "primordial fireball" (ha ha). The campfire is relatively tame compared to meteorological temperatures, which many plants and animals use to understand time. Because fluctuations are so small, the CMB is often described as a near-perfect blackbody, see also: www.astro.ucla.edu/~wright/CMB-DT.html .
Please elucidate in a little more detail for the benefit of the unwashed!
In a previous life, I was tasked with menial programming, and accumulated some bad karma by skipping work to go and visit the GSFC library. Personal complaints aside, one outcome is that I can recommend the author Joseph Silk if you want to read more interesting books about cosmology. He is pretty good to listen to at a beginner or intermediate level. --Brad