Luminosity distance DL is defined in terms of the relationship between the absolute magnitude M and apparent magnitude m of an astronomical object.
The relation is less clear for distant objects like quasars far beyond the Milky Way since the apparent magnitude is affected by spacetime curvature, redshift, and time dilation.
Calculating the relation between the apparent and actual luminosity of an object requires taking all of these factors into account.
The object's actual luminosity is determined using the inverse-square law and the proportions of the object's apparent distance and luminosity distance.
In a spatially flat universe, the comoving transverse distance