Eru Ilúvatar or "The One" is the single omniscient and omnipotent creator in LotR Mythos. Ilúvatar = "All Father" in Quenya. So he is the "All Father" of Pagan Mythos, but there is a heavy Neoplatonic theme here too. Let's take a deeper look...

...so first things first. No, this is not the Christian God whom is a Trinity. There is no Son, or "Holy Spirit" here. This is a Neoplatonic concept of "The One" also taught by Pythagoras. I think Tolkien was influenced by Manly P Hall on this one...(from Secret Teachings...)

...so Manly P Hall took a Neoplatonic approach to Norse Mythos and his book had a big influence when it came out. Right around the same time Tolkien was writing too. So "All-Father" is the supreme creator deity above the Aesir (In this interpretation). Its "The One" of Plato.

...so the Cosmos is based on Music like Pythagoras said. The creative Good being the Harmony/Order. The destructive Bad being the Discord/Chaos. Its not Good and Evil per say, its Harmony vs Discord. Its different from the Christian idea of Good vs Evil.

..In the Neoplatonic sense the Cosmic Gods are below "The One" and are really more of Regents over the Material World "Middle Earth." They are a part of the Musical Harmony. The way I like to think of this...

..Is the White Light being the Harmony. Each Color on its own is beautiful, but combine them together and you have the Harmony of Light. The Cosmic Gods being like each distinct color. Anyways probably not the best analogy, but moving on...

...so the struggle of Melkor vs The Valar is about Harmony vs Discord. NOT Good vs Evil. The "Evil" is really just the absence of Good (Plotinus). Melkor and Sauron too, were not originally Evil. Their Goodness just became less and less until it finally vanished altogether.

...and Melkor became pure discord. He seeks to disrupt the Harmony. He is a force of Distortion. The Orcs are just a distorted version of the Elves. Trolls a distorted Ent. He cannot create, he can only distort.

...so in closing. Is the Cosmology of Middle Earth "Christian"? No, Not at all. Its a Neoplatonic twist on Norse Mythology.