This is a bit outside my expertise, so anyone with a good knowledge of the appropriate physics would be nice. Just thought of an unusual world concept to go along with all those people who dream of ringworlds, Dyson spheres, and such.
My idea: A binary planet (a pair of binary planets?), er, two masses that orbit each other, have roughly the same size and mass, and keep the same face towards each other. The potentially interesting aspect: The inhabitants of one planet build a space elevator connecting to the other one.
It's my understanding that our moon keeps the same face towards us because of its origin as a torn-out chunk of Earth. Seems to me the right circumstances could divide a planet evenly. Of course, I realize this, along with the chance of making both halves life-sustaining would be wildly improbable, but it's a big universe, and a potentially cool setting helps.
So, any difficulties to discuss? Stuff that comes to mind: 1. Even if life develops on both places, the two would be quite different. 2. The two faces might not be synchronized enough to support an elevator for long. 3. Routine eclipses might make for interesting, though potentially nasty climates.