I have never come across a paper that describes door-squeaking theory, but I can take a guess at why doors squeak.
If you have read the article How Acoustic Guitars Work, you know that a guitar string vibrating on its own doesn't make very much noise. When you attach the string to a guitar's soundboard, however, the sound is much, much louder. In a door hinge, the hinge's pieces of metal are sliding over each other and vibrating. The door attached to the hinge probably acts as a soundboard to amplify the sound.
I do know how to fix the problem. If you take the door off its hinges and rub wax from a candle on the pins and on the places where the hinges touch each other, the door should open in complete silence!