Is living on an Alderson Disk possible? An Alderson Disk is a large CD-like megastructure, with a star in the center. If the disk is thick enough, it could have its own gravity. Also, the star in the center can bob up and down, resulting in an artificial day/night cycle.
What are the limitations set by this world design? Any help is appreciated!
An Alderson Disk suffers from almost all of the same problems that a Niven ring world does and has a couple unique to its configuration.
Instability
One problem is that the structure / star configuration is dynamically unstable. If you perturb the disk / toroid (by say a meteor strike), then it will most likely (eventually) hit the star - to the extreme detriment of all disk inhabitants.
Therefore, the disk will require an active control system able to restore the disk (toroid) back to its desired location relative to the star if something perturbs it.
Gravitation
One bit problem the disk has that the ring world doesn't is gravitation. The disk provides no mechanism for keeping things "stuck to the surface".
If you wish to make the disk massive enough to supply its own gravitational field then you end up with a toroid whose cylindrical cross section is that of Earth's in both dimension and composition.
The problem is, we haven't mastered the use of materials able to resist isostacy (returning to a spherical shape) under those conditions. Rather than simply supplying a force to keep people stuck to the toroid's surface, it would supply enough force to collapse the toroid into a (large) ball of matter - much to the dismay of the toroid's inhabitants.
The extremely bad news about this is that you can't magic the problem away with fantastically strong and lightweight materials. You need that mass for its gravitation and it's the combination of mass and gravitation that will collapse your toroid.
Good news
Unlike the ring world concept, if you built a self-gravitating toroid, you wouldn't need to spin it to keep things stuck to the inner surface. This significantly reduces the strength of materials requirements (but doesn't get rid of the problems stated above).
Realistically
I can't see any way to enable this to work nor can I foresee any unless we fundamentally alter our understanding of the Universe.
But if you have your heart set on the design, just include the fiction changes required to make it work. I think an extremely light weight design with gravity generators would work (until someone shuts off the power). You'll want some fail safes, along with fail safes for your active stabilization system to keep the toroid/disk from contacting the surface of the star.
As a general rule, gravity pulls you to the center of gravity of the most gravitationally influential object for your position. In this instance, it seems like it would be the ring. The center of gravity for the ring is... somewhere in that star. This means your people, unless they have things to brace themselves against, will fall into the star. Given that a habitable zone is usually on the order of ~1 AU for a star like ours, I'm willing to say that this will very likely be the case.
Vsauce did a video on a "flat earth" which has a simulation of a flat earth. It displays the problem with living on any disk-like object; the further from the middle you are, the more gravity pulls you to the center of that disk and less to the ground you're trying to walk on.
If the disk was spinning, it would not change the center-of-gravity for the disk. People would still fall into the middle unless they were at a very specific radius, where the acceleration provided by the disk/star's gravity forces them to essentially orbit the star. If you go too far to the edge or center, you'll fly off of fall in.
The best way to overcome this would require a disk that was much, much thicker than it is wide. Alternatively, your disk would need to be infinite in diameter to allow for equal gravity all along the disk. If you're willing to have a structure of nonuniform density, you could make the habitable zone much more dense (and therefore gravitationally stronger), but this still may not work because of that tricksy center-of-gravity.
What about this "infinite sheet approximation" people keep talking about, claiming that the gravity "close" to the surface would feel normal? Well, that's called the infinite sheet approximation, which is more often used in electromagnetism, but can be used in gravity. It turns out that this approximation is only good as long as the distance between you and the sheet is about 1/5 of the distance between the point below you (on the ring) to the edge of the sheet. So if your ring has a thickness of 1 au, your infinite sheet approximation works for 1/5 AU above the surface in the middle of the ring. If you're 1 m from the edge, the infinite plane approximation only holds to about 1/5 of a meter.
There is also the slight problem of that sun drifting into the side of your disk. Due to the fact that it is surrounded by an equal amount of material in the plane of the disk, it can drift around in that plane as if the disk wasn't there. (It's the 2-d case of gravitational force inside a shell.) This means your sun could very easily run into the inner radius, which I imagine would cause problems.
There are also some problems with tidal forces; the inner radius of your disk will experience more pull from the star than the outside of your disk. Unless the material is strong enough to withstand these forces, the star could rip the disk apart. Of course, the proposed disk is large enough that I think it must be made out of some magic material.
Like Niven's Ringworld, the Alderson disk would have to be made of unreasonably strong materials (the super materials "Scrith" and "General Products" spaceship hulls were made of materials which had the strong nuclear force enhanced.) Outside of science fiction, a super civilization might be able to manipulate neutronium, which is also dense enough to provide gravity for the inhabitants of the disk, assuming the inhabitants were the size of bacteria and comfortable with a surface gravity measured in thousands or millions of g. I suspect that amount of gravitational pull on the equator of the star would pull it apart as well....
The Alderson disk should really be thought of as a sort of thought experiment, rather than a real thing. If you want something like an Alderson disk, perhaps you could follow the example of Forest Bishop, who scaled the Ringworld down to something that could be built from real materials. A Bishop Ring has a radius of 1000km, a width of 500 km and the atmosphere is held in by a combination of centrifical force due to the rotation of the ring, and walls on the edges of the ring that are 200km tall. A system of mirrors reflects sunlight over the walls and onto the surface.
Your "CD world" would use a fusion lantern or a "disco ball" like target for the solar mirror platoon to provide light, and a large disk to provide the surface area. Air and water on the surface would rapidly escape into space unless there was some sort of "roof". Perhaps a huge, transparent cover made of diamond or similarly hard and transparent material could be constructed to cover each side of the disk (giving the term "jewel case" a whole new meaning). The maximum size would depend on the materials used, but Graphine, Fullerines and other materials of that nature would allow you to make structures measuring hundreds or thousands of kilometres in diameter.
One problem is gravity. For people to be pulled down, the disc will have to be very thick. At that level of thickness, one has to make sure that the material but the disc is composed of is strong enough to avoid collapsing on itself. Also, relying on the bobbing of a star for a day/night cycle is very unreliable. Getting it to bob steadily would en difficult. Also, a bobbing sun would contribute to what I will discuss below. Most of all, they would die. This is because the gravitational equation is an inverse square law. If the sun is not perfectly in the center, the gravitational pull will be weaker on one side and stronger on another. This will result in the disk crashing into the sun. One might say that as long as we do not service star, it will be perfectly in the center. This is not the case. No one can perfectly put the star in the center. Even if extremely close, over the eons it would slowly crash into the sun. Even if they could put it perfectly in the center, we must remember that the sun is not static. It is solar flares and their comments and other disturbances all throughout the solar system. These things would cause it to not be perfectly center.
You need enough forces to keep the Alderson disk from collapsing in on itself. Let's assume a thickness of 6000 km, with 1000-km walls on either face around the interior rim made of tungsten, which has a melting point of 3695 K, and we'll assume that it has an albedo of 74%, and the sun at the center is just like Earth's. We can safely place the inner rim at .01 AU, but we will need to deal with the gravitational force exerted by the sun. Let's put the walls at 1 km thick, which means that they'd have a total mass of 1.4510^24 kg, and as the mass of the sun is 1.9810^30 kg, the force would equate to 8.5610^25 N. The pressure would be 1.1410^9 Pa, and that is for the walls alone. If we want some semblance of a habitable zone, we would need to have it stretch all the way to 1 AU, and we will assume that the rest of the material has a mean density of 5515 kg/m^3.
The total mass of the structure would be about 4.6110^31 kg, which means that the force of gravity on the walls would be 2.7210^33 N. No known material could support such a force, so you will need to work with something a good lot stronger than anything we know. The material's incredible strength would also create some pretty bizarre gravity. At the inner and outer rim, ignoring the sun's gravity, gravity would be about .560 N/kg, and when you factor in solar gravity, the outer rim's gravity is .566 N/kg, and if you were to stand at the inner rim, you'd fall into the sun. As for the middle of the faces, the gravity is 341 N/mg, which would be impossible to survive in. In between those two extremes, there would definitely be some sort of region where there's just enough gravity, but I've made a lot of assumptions.
An array of mirrors and lenses could be used to make sure that there are regions that get just enough heat and light for life to exist, and have a suitable amount of gravity. But, we would need to bend the laws of physics a good bit for an realistic Alderson disk.
