The Dyson Shell is the form of Dyson Sphere that is most commonly depicted in science fiction. This is a real shame, because the Shell is the least feasible and most unstable version of the Dyson Sphere concept.
The Dyson Shell is a huge spherical "egg shell" surrounding a star.
In fiction, it is usually depicted as having a livable habitat on the inner surface, facing the sun. This livable surface is rather silly, however. The gravitational center of the sphere would be roughly in the center of the sun. Someone standing on the inside surface would either float weightlessly, or fall towards the sun, depending on how far the inner surface of the shell was from the sun. The same thing would happen to any atmosphere you tried to put on the inner surface, it would gradually be lost into the void between the shell and the sun. These issues could be partially solved by spinning the shell, which would generate centrifugal force that would simulate gravity perpendicular to the rotation along the equator. The poles would have no such artificial gravity, and life would only be possible near the equator. Life would be contained to a narrow band similar to a Niven Ring, but the other regions of interior surface could be used for solar collection.
If the life was placed on the outside of the Shell, you'd solve the gravity issue (as the sun's gravity would hold you and the atmosphere to the surface), but you'd be trading it for other problems. For one thing, you'd have no light, as the shell would absorb all the light of the sun.
Even if solutions could be found to those issues, you'd still have to face the instability of the shell. Since the shell extends around all sides of the sun, it has no net gravitational interaction with the Sun. It doesn't orbit the sun, it merely free floats near and around it. Without some propulsion system for course-correction, there's a high likelihood the Shell would eventually drift into contact with the sun. The pressures exerted upon the Shell would exceed the resilience of any known construction material. And then there's all the complications of trying to build such a thing. There's enough usable matter in our entire solar system to build a Dyson Shell (whose surface is as far from the sun as our own planet is) between 8 and 20 cm thick, and that only if we mine all the planets. Where does humanity live while all the planets are being stripped (down to gas) for building materials?
Of course, none of that means it's impossible for some Sufficiently Advanced Aliens to build a Dyson Shell. When you've got tech that borders on magic, you can certainly expect to overcome limitations that would stop modern man. However, any civilization advanced enough to build a Shell would have zero need to do so. If they need energy, they can get it in easier ways - they can build a Dyson Swarm or Dyson Bubble much more efficiently. If they need real estate, they can colonize other systems more readily than build a habitable Dyson Shell. It would seem the only reason to build a Dyson Shell instead of some other form of Stellar Megastructure is because you needed the challenge.
Game and Story Use
- A Dyson Shell would be an expression of a truly powerful or decadent civilization. Any "sane" society would have built some simpler Megastructure that fulfills all their needs - but these godlike beings have nothing better to do.
- An ancient and abandoned Dyson Shell built by the Precursors is collapsing into it's star. It's only a matter of hours before all that Lost Technology vanishes forever. How much can the PCs save from the fires?
- Even more impressive, a red giant star suddenly appears out of nowhere - in fact, it has outgrown a dyson shell that was wrapped around it by some precursor civilisation, a shell so efficient that the outside was not noticably above the cosmic background. What the hell happened to make such a powerful species vanish like that (assuming that they have) and, given that it would be truely wierd to put a shell on a star close to expansion, what has the shell been doing with all the energy whilst its creators have been away? Are there any more shells like that in apparently void areas of space?
- For more ideas, see Stellar Megastructure and Dyson Sphere.