http://www.runegild.org/BlackSunAnalysis.pdf

In esoteric Runelore the figure makes 3 swastikas which represent Arising, Being, & Passing Away to a new Arising.  Such as the solar eclipse represents the death of Osiris and the rise of Horus.

Found on the Norse Pagan band Non’s Website –

“There is a black sun which is not visible to the human eye.
It is our beacon and its fire burns within us” – Akkadian temple inscription

Image of Black Sun ring from

http://www.europaltd.com/

The Black Sun however seems to sometimes (mostly) but not always be associated with the Dark Left-Hand path of Satanic and similar cults as the “negative” version of The Star or The Sun of popular esoteric philosophy.

Ancient eclipses had very powerful effects on the history of the human race. It was traditional seen as a bad omen. The word “eclipse” is derived from the Greek, “ekleipsis”, which means “omission” or “abandonment”. In Chinese it is “shih”, which means, “to eat up”.  (again refer to section on Evil regarding the absence of God).

In alchemy, the black sun, or “sol niger,” represents the dark, destructive aspects of the sun.

From a description of the Icon of the Annunciation:  The black sun in the upper part of the scene represents the essence of God, indefinable and unknowable; the rays represent His energies (in the form of the Holy Trinity) which are manifestations of His essence and can therefore be known.

This icon represents the Annunciation, that is, the moment when “The angel came in unto (Mary), and said, Hail, thou that art highly favored, the Lord is with thee, blessed art thou among women. And when she saw him, she was troubled at his saying, and cast in her mind what manner of salutation this should be. And the angel said unto her, Fear not, Mary: for thou hast found favor with God. And, behold, thou shalt conceive in thy womb, and bring forth a son, and shalt call his name JESUS.” (KJV, Luke 1: 28-31).

For some alchemical explanations of Sol Niger in relation to The Sun card of the Tarot review http://www.cs.utk.edu/~mclennan/OM/BA/PT/M18.html

http://www.shadowplayzine.com/Articles/pluto.htm

In Western Kabbalistic Tradition, Persephone and Hades are first encountered on the path between Malkuth and Yesod with Hecate as guardian of their Mystery. Pluto/Hades in his dark glory (the Black Sun or shadow-self) and Persephone as Queen of the Underworld, ruling death and rebirth (the bright-self) are to be encountered on the path between Yesod and Tippareth. These two paths lead to the “hidden riches” within the individual. The paths form part of an ongoing series of confrontations which are resolved in the process of attaining internal balance. This balance is to be found in the dance of energy which is poised at the knife edge between the forces of darkness and light, a manifestation of the power of Pluto.

Agrippa’s thought unites the streams of classical Neoplatonic and Hermetic philosophy, Jewish Kabbalah and Christianity. Three Books of Occult Philosophy, his most famous work, is a systematic exposition of the occult, in the sense of hidden, knowledge extant in Renaissance Europe. It is an encyclopedic work of Renaissance magic providing information on such diverse topics as planetary rulerships, occult virtues, sympathies and enmities of natural things, enchantments, sorceries, types of divination, the scales of numbers and their significance, astrological talismans, the divine Trinity, the Kabbalistic Names of God and the orders of evil spirits.
Yet despite its comprehensive nature Three Books of Occult Philosophy is organized in a systematic fashion. The three books each correspond to the three worlds of the elementary, celestial and intellectual realms. Agrippa sees the descent of all things from God through the worlds as a hopeful sign of the possibility of an ascent back to God.
The Renaissance philosophy of magi like Cornelius Agrippa represents the highest development of a spiritual and unified schema of thought in the West prior to the advent of the materialism and atheism of the Enlightenment. After 500 years Three Books of Occult Philosophy remains one of the leading texts of Western esoteric thought.

Three Books of Occult Philosophy Bk. II, Chapter 52, (Tyson ed.) page 410.

This reminds me of the Kabbalah – sideways…