tolkiens legendarium - Was the Eye of Sauron a physical or metaphorical manifestation of Sauron's will?

There he took up again his great Ring in Barad-dûr, and dwelt there, dark and silent, until he wrought himself a new guise, an image of malice and hatred made visible; and the Eye of Sauron the Terrible few could endure.

The Silmarillion, Akallabeth

and 

There now he brooded in the dark, until he had wrought for himself a new shape; and it was terrible, for his fair semblance had departed for ever when he was cast into the abyss at the drowning of Númenor. He took up again the great Ring and clothed himself in power; and the malice of the Eye of Sauron few even of the great among Elves and Men could endure.

The Silmarillion, Of the Rings of Power and the Third Age

Which serve to destroy the palantir theory as they refer to Sauron's reoccupation of Barad-dur in the Second Age. They do I think, support the idea of the Eye as a physical presence.

In fact with every step towards the gates of Mordor Frodo felt the Ring on its chain about his neck grow more burdensome. He was now beginning to feel it as an actual weight dragging him earthwards. But far more he was troubled by the Eye: so he called it to himself. It was that more than the drag of the Ring that made him cower and stoop as he walked. The Eye: that horrible growing sense of a hostile will that strove with great power to pierce all shadows of cloud, and earth, and flesh, and to see you: to pin you under its deadly gaze, naked, immovable. So thin, so frail and thin, the veils were become that still warded it off. Frodo knew just where the present habitation and heart of that will now was: as certainly as a man can tell the direction of the sun with his eyes shut. He was facing it, and its potency beat upon his brow.

The Two Towers, The Passage of the Marshes

The important point here is that the Eye has an actual physical impact on Frodo. It bows his head and can be felt as a malignant sun on the body.

The Eye of Sauron has always fascinated me for a long time in the way it's used in a metaphorical sense then in some senses as if some characters actually saw and felt an eye watching them.

Which is it? Is the Eye a physical entity, or a metaphorical one?