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[Middle Earth] Is Sauron ever physically present during the Lord of the Rings?

I'll preface this by saying most of my Tolkien knowledge comes from seeing the films and reading the hobbit ten years ago. So Sauron is killed in the prologue, and he lingers about for two and a half thousand years, presumably through the one ring action g as a sort of horcrux. He then appears as the spectral necromancer in the hobbit, and is defeated by the white Council. After that, he is building up his power in mordor. How is that? Is he even physically existent? Or does he take hosts, or communicate like a ghost would? What is the eye of Sauron? Is that the form he takes? If so that's rather shitty. Who or what is the witch king, and why is he involved? Than you in advance, I really just don't know much of anything, and I ask about the witch king because as a kid, I thought he and Sauron were one and the same.
gpt
>So Sauron is killed in the prologue, and he lingers about for two and a half thousand years, presumably through the one ring action g as a sort of horcrux.

Pretty much, though it's Sauron's power rather than his soul that's kept in the One Ring.

> He then appears as the spectral necromancer in the hobbit, and is defeated by the white Council. After that, he is building up his power in mordor. How is that? Is he even physically existent? Or does he take hosts, or communicate like a ghost would?

Sauron's physical form was killed in the War of the Last Alliance, but he had rebuilt it by at least the time of LotR (if not much earlier). During both time periods, he took the shape of an unnaturally large but not gigantic humanoid. So he was physically present in Barad-dur during LotR, but Sauron is not the kind of guy who fights in battles unless he has to. During the War of the Last Alliance, Barad-dur was under siege for 7 years before Sauron decided to enter the fight.

> What is the eye of Sauron? Is that the form he takes? If so that's rather shitty.

The Eye of Sauron is a symbol of Sauron's power and watchfulness; it is no more a literal description of him than the White Hand is of Saruman.

> Who or what is the witch king, and why is he involved?

The Witch-king is the greatest of the Ringwraiths, the humans who were given the Nine Rings by Sauron and who were corrupted into wraiths. Besides the Witch-king's natural abilities as a 4200 year old sorcerer and wraith, he was given an extra "demonic force" by Sauron during the later parts of LotR.