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The "Light-Year City" Questions — What would be the gravitational implications of a city in the far, far distant future, with an area spanning one square light year (3.456 × 10^25 mi² area)?

This question has been broken up into sub-topics, the other questions related to this idea are listed here:

Governmental Implications of a "Light Year City"

Technological Implications of a "Light Year City"

Premise: Imagine a city floating in space like a fabric, that is so vast and immense, it spans one square light year in size. For perspective, the Milky Way has a diameter of roughly 10^5 lightyears, so if we plug that into A = pi(d/2)^2, the Milk Way has an area of about 7.8 billion LY^2. So against a galaxy, the area of this city very small. The difference here is that in a galaxy, the matter is pretty spread out, but densely packed in small groups of solar systems. In a "Light-year City", the matter is much more densely focused in one square light year.

Question: How would a city of this proportion need to be organized, in order to deal with such gravitational concerns? What might be some technological developments that deal with gravitational issues? What would the epicenter of the city be like, having so much matter coalesced around it? Other gravitational thoughts?

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  • $\begingroup$ Why would the population density be high? Given such a massive area in a city (which brings to mind utility hook-ups and public transportation through all of it), the density will likely be extremely low. $\endgroup$ – Michael Richardson Nov 2 '16 at 20:44
  • $\begingroup$ The exorbitant distances might be a motivating factor. Perhaps the city being a LY*LY in size is dependent upon the population size. But thats a great interrogating question that I hadn't thought of yet. $\endgroup$ – Ian Nov 2 '16 at 20:48
  • $\begingroup$ 1) Why this city is supposed to be square? I mean a bit more practical to keep the same population in something 3d instead of 2d? 2) Problems? Being ungovernable because of huge population and delay caused by transfer data at speed of light... $\endgroup$ – Shadow1024 Nov 2 '16 at 20:51
  • $\begingroup$ @Shadow1024 Sorry for the confusion. A square light year is simply a measure of the city's area, but not necessarily a description of its geometry. $\endgroup$ – Ian Nov 2 '16 at 20:53
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    $\begingroup$ You may need to describe exactly what you mean by the area. Is it set on an infinite plane? Some kind of space station? How large is it in the 3rd dimension? $\endgroup$ – Michael Richardson Nov 2 '16 at 21:02
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Even if the city was only 1km thick, it would contain a noticeable fraction of the matter in the observable universe. If the city had the same density as the earth, it would have a mass of ~$5\times10^{41}$g, and the universe is $3\times10^{55}$g. As there are $10^{11}$ galaxies, this would mean the city was the mass of a galaxy.

It would cause terrible gravitational problems to itself; in particular, there would be immense pressure for it to collapse inward to the center, where it would become a giant black hole. That it isn't a sphere means it couldn't be stable. If it was a sphere, it would require more matter than the universe has.

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  • $\begingroup$ Can you share your work on the math? Great answer! If this is correct sounds like they would need to do some sort of "gravitational easing" to deal with the enormous gravity. Perhaps they've developed a higher understanding of physics such that they can manipulate the strength of gravity in a locus. $\endgroup$ – Ian Nov 2 '16 at 21:22
  • $\begingroup$ @Ian If it were a sphere it would be a black hole and be crushed out of existence. $\endgroup$ – Loren Pechtel Nov 3 '16 at 20:10
  • $\begingroup$ @LorenPechtel can't be crushed out of existence, law of conservation of matter. If it exists it stays $\endgroup$ – Ian Nov 3 '16 at 21:23
  • $\begingroup$ @Ian Existence as a city. It would become a singularity in the center of the black hole. $\endgroup$ – Loren Pechtel Nov 4 '16 at 0:44
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The most logical way to make a 'city' this big is to inscribe in onto the surface of a 3-d object. A sphere comes to mind, especially since the Dyson Sphere or Swarm is a well worn topic on this site, with some existing excellent answers.

Since the surface area of a sphere is $4\pi r^2$, we can solve backwards for the radius of a sphere with surface area 1 ly$^2$, which gives us $\sqrt{\frac{1}{4\pi}} = 0.28 \text{ ly}$.

To minimize the gravitational implications, you would want to construct this system as a set of orbiting surfaces at 0.28 ly from a star. As was previously noted, these surfaces can't be that massive (i.e. not too deep) or else they will require a galaxy of construction materials. The other concern is finding a star that puts out enough energy to supply a surface at 0.28 ly away (almost 600x farther away than Neptune). There are plenty of super powerful stars out there, you'd just have to find one that is going to be stable long enough to make building this structure worth it.

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How about a totally different approach to your city:

We still need handwavium to build it but we can avoid the gravitational problems. You said "flat" but I don't think the occupants will mind my answer: Build a cylinder 1ly long and 1/2π ly in diameter. You have a square light year on the inside of the cylinder. If I haven't dropped a zero somewhere (why do so many web calculators refuse scientific notation??) the spin needed to maintain 1g outward is only a little over .1c.

The city will still be flat to it's occupants but the sky will always be looking upon the other side of the city (although too far away to resolve anything, it will just be a lit area.) Spin effects should not matter. Since it doesn't have gravitational mass it's actually easier to come and go and you can boost on a track rather than in a starship.

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  • $\begingroup$ handwavium. i like this idea. $\endgroup$ – Ian Nov 3 '16 at 21:25
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Whatever you want?

This should really be a comment, but your question gives nowhere near enough data for us to guess. I'll still write this as an answer as it means I do not need to worry about character count and, more importantly, having even a partial list of the relevant issues might be what you actually need.

First, and this is pretty important, what kind of surface gravity do they have? If they have anywhere near one G on what is essentially two dimensional structure, they absolutely will have gravitic super-science that is affordable and extremely reliable and stable.

It is in theory (I think, not doing the math) possible to build a structure that is like sheet in large scale and thick enough to have normal surface gravity on both of its surfaces, but the kilometer Mathily assumed would not be anywhere near enough for that. Not that the few extra orders of magnitude would really have any effect on his conclusion.

And if they are controlling the gravity with advanced gravitics anyway, the "gravitational implications" would also have been designed by the engineers ("gravitics" + "architects" -> "gravitechs"?) who designed the structure. So you would get the implications by thinking about what the builders goals were when designing the structure.

I can't really speculate on that since I do not know your setting, but I'll say it would take very convincing reason for the structure to be that flat when the tech would allow them to spread the surface area over some complex 3D (or even with few extra dimensions, if their tech is good enough for this) shape. So it should IMHO be more like a ball of thread with cross-links than a sheet.

But I am sure there are lots of plausible reasons they'd make it flat instead, if that is important. Just saying that you'd need to supply one. Even something like "the builders were really weird" would be enough.

The other option is not to care about surface gravity or to supply it as needed with spin habitats. In this case the density would be much lower than what Mathis assumed. Probably below the density of air with vacuum between habitable areas. It would really be a very thin and sparse web of very thin strands.

Even then I do not really believe your desired shape of a 2D sheet can be made stable. The structure is just too big and a sheet is simply too unstable a shape. Probably a good thing as it is also pretty inefficient for logistics...

Something like a thin ring rotating rapidly around its center of mass, maybe? Make the strand the ring is composed of hollow and make them rotate and the inner surfaces of the strands might be habitable and have the proper magnitude of combined surface area.

Super-science is probably closer to what is wanted?

I apologize for an answer that doesn't really even try to answer your question, but I hope it is useful.

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  • $\begingroup$ Whatever you want is essentially the idea. $\endgroup$ – Ian Nov 2 '16 at 22:19
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Intended to be a comment, but bad habit to remove comments and move them in to chat, limits etc

Primum, OP should take look at Isaac Arthur , Megastructures - it is just obligatory to watch in chronological order, I conclude that based on his comments.

Secundo, I have to address 2d vs 3d solutions.

All available surface of that 1ly2 city, can be packed in way much smaller 3d structure, but there is one argument against it - less outer surface you have, less energy you can use inside of that object.

Even kingledion suggestion will use 2 times less energy then flat one, because flat one have 2 emitting surfaces, sphere will have only one, if mass of solutions is the same, so it is 2 times less efficient per mass of the construction.

This way there are arguments why someone may like to build flat, instead of more complex shapes.

However OP is controversial here:

  • Imagine a city floating in space like a fabric - look like a flat surface to me, or not a flat surface

  • A square light year is simply a measure of the city's area, but not necessarily a description of its geometry. - looks like a sphere to me.

someone asks - Why would the population density be high? Answer is simply, because a human need about 10kW 24.7.365 or less for his needs, so potentially this city may have 1 human per about 20 square meters of outer surface, and it is a tiny bit denser then Top1 from the list List of cities by population density, so probably it depends on definition of what we should call as high population density.

Yes, OP have to define how much people he want, how much energy they should use, which shape of city should be etc.

However, I should point a flat city of this size is possible, and I would estimate its mass as less then 1/1000 of milky way mass, significantly less(orders of magnitude, about 10t or less per human). Depends on technology, implementation may be different, but for gravity I suggest space habitats approach(rotating small block with 20-200 millions of people inside, it may also help with management organization, which is another OP's Q).

Amount of the energy they may use, it will be about 1/1000 of milky way's energy production.

Flat is ok as shape, twice of energy dissipation per same mass it a good deal, in situation where they should dissemble 2 times less of other star systems.

Also I recommend to build it near Massive Black hole, it will help them to solve energy problems, maybe star going to be supernova will be a good place to start as it will give significant boost on initial stage by giving the energy needed to operate/manipulate with other stars, although you should be a bit better prepared then it mention in that answer, have enough active matter.

Super massive Black hole would be perfect place for the city too.

But first of all you have to decide what is the goal of the city, what wish they(citizens) to achieve? Answering that question may determine what it should be, and it will do that better, then answering a question - how can I have a object with impressive size.

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Okay regardless of the material this city is made of it will have to be built in an artificial gravity field of some description or it will undergo hydrostatic collapse and turn into a solid sphere which will be... messy... for the inhabitants. Given that it has to be built under artificial gravity it can be made "flat to the senses" without actually being particularly linear in reality. Gravitational flatness is a prerequisite to building the structure at all, this will mean that your inner ear doesn't know any different and you won't have an atmospheric gradient to create any kind of altitude effects. Visual flatness will require long surfaces to curve slightly downward, possibly into a loop, using only one side for habitation, to appear flat; the human eye perceives large flat surfaces as concave. The Greeks had a number of architectural tricks involving subtle curves that fooled the eye into thinking things were flat, these were necessary because actual flat surfaces don't look flat. The centre would be no different to the rest since the gravity is artificial, you're going to need to manipulate gravity waves either directly or by using virtual mass to do this. A raft of technologies have been proposed by different writers for this such as Wil McCarthy's Collapsium which can be stablised into linear structures using fractal balancing of the forces between it's constituent mass nodes, or my favourite David Brin's Cavitronics used to create virtual mass from raw space-time it has so many many uses and implications.

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