Black Sun
In all this talk of the different suns, what about the Black Sun?
In The Sword of the Lictor, when Severian is in Thrax with the sick children, he says that the Conciliator is the Black Sun.
"That night in the jacal it [the Claw] was not brilliant, but it glowed with so deep a blue that the light itself seemed almost a clearer darkness. Of all the names of the Conciliator, the one that is, I believe, least used, and which has always seemed the most puzzling to me, is that of the Black Sun. Since that night, I have felt myself almost to comprehend it." (Volume III, Chapter VIII, TBotNS)
"Black Sun" makes me think of a black hole, but I don't see what that has to do with the Conciliator. Maybe someone else does?
The only thing I can think of is the darkness at the crucifixion of Christ, which is thought to have resulted from an eclipse:
Luke 23:44-45
And it was about the sixth hour, and there was a darkness over all the earth until the ninth hour. And the sun was darkened, and the veil of the temple was rent in the midst.
Mat 27:45
Now from the sixth hour there was darkness over all the land unto the ninth hour.