The Black Sun is a mathematical point that corresponds to the Sun when it is furthest from the Earth. On July 4th the Sun is Aphelion, furthest from the Earth, and on January 3rd, the Sun is perihelion, closest to the Earth [estimated to be 147.5 million kilometres]
It has nothing to do with the burnt out Sun that was rumoured to be the source of the power of the Aryan race in the past. Although according to esoteric literature and a Kryon channel Earth had two suns originally.