What is this huge symbol on the door in the Truth realm and in the Neon Genesis Evangelion opening?
It's a slightly modified version of the Sephirothic Tree of Life as defined by Robert Fludd, who was a physician with interests in Kabbalah and other religious mysticisms. The globes (called Sephiroths) are thought of as being ways in which the universe shows its truths to humanity. They're also printed with the words God used in creating the universe in Genesis.



You can read up on it more here, but the basic idea behind it is that it is a mystic symbol representing universal truth -- and the Truth is on the other side of the door in FMA.

In NGE, however, the symbol appears after the Mass Production units form an inverted tree of life, symbolizing the opposite of creation -- destruction, death -- after crucifying Eva 01. This is part of the Third Impact, in which nearly all of humanity is reduced to LCL. You'll find that there's a lot of mystic symbolism in NGE.