Question: This is a spectrum of a high-redshift QSO discovered by the Sloan Digital Sky Survey. The large emission line is Lyman alpha (rest wavelength 1216 A). What is the redshift of this QSO?
The framework: geometry plus dynamics
Use of R-W metric for light rays
Integrate along two path lengths
Calculating volume in a curved space
Analogy with volume element from 3D spherical coords in flat space
Using the R-W metric to give us the three components of the volume element
Integrate out to radius r, over all theta and phi
