* No Atmosphere: The Aurora Borealis is caused by charged particles from the sun interacting with a planet's atmosphere. The moon has virtually no atmosphere, so there's nothing for these particles to interact with.
* No Magnetic Field: The Earth's magnetic field acts as a shield, directing these charged particles towards the poles. The moon has a very weak magnetic field, so it can't create the conditions necessary for auroras.
While the moon doesn't have auroras, it does have a faint glow called "moon glow" which is caused by sunlight reflecting off its surface.
