A recent article details the cost, materials, and time it would take to build a Death Star.
After careful analysis of their assumptions and conclusions, diving into the depths of my knowledge and experience as a mechanical engineer, I've determined that with some modifications to the design, it is completely possible for private industry to build a Death Star, and they could start tomorrow!
First, let's go through the article's assumptions. They estimate the size of the Death Star to be a sphere 140km (87.5 miles) in diameter and to be of an average density equal to that of a typical aircraft carrier. They determined that there is enough steel within planet Earth to build 2 million Death Stars, but we only need one. Using today's annual rate of steel production (1.3 billion tons/year) it would take 833,315 years just to generate the steel. This figure does not include actual construction time. The cost would be roughly 13,000 times the world's GDP at 2012 material prices.
Safe to say, no one is building a Death Star, yet.
However, there are a few problems with their assumptions. For starters, if the Death Star is 87.5 miles in diameter, then it would be quite difficult for personnel to move throughout. As we saw in the Star Wars movies, the center of the sphere is dominated by power generation, so any mass transit within the Death Star would have to travel the long way around the circumference. It seems unnecessarily large, but we'll keep the size assumption for now.
The Death Star also doesn't need to be the same density as an aircraft carrier. The hulls of ships are hit with massive hydraulic forces as they travel through water and get hit by waves (not to mention torpedoes!). They also are under tremendous pressure from the weight of water pressing in all around them. For example, a Nimitz class carrier is about 244 feet tall. Assuming that a third of it is below the water line, the pressure at the bottom of the hull is roughly 52 psi, comparable to the air pressure in a champagne bottle or a bit truck's tires. The Death Star, on the other hand, operates in a vacuum where there no external pressure and internal pressure is only as high as it needs to be for humans to survive (about 14.7 psi).
Furthermore, there are ways to skirt some of the more unnecessary requirements of building the Death Star that make this project much more feasible. For starters, the Death Star has a force field beyond its normal ballistic shield (which was disabled on Endor in Stars Wars: Return of the Jedi, if you remember), which enables occupants to open the doors to the ship dock without anyone getting sucked into the vacuum of space. Given the existence of this technology, a steel skin hardly seems necessary.
Bigelow Aerospace has been experimenting with the concept of inflatable space modules. Since the interior is at atmospheric pressure, and the exterior is a vacuum, these fabric modules expand outwards. The fabric will be much lighter than steel, and when not in the vacuum of space, folds up neatly inside the cargo hold of a space shuttle, making it much cheaper and quicker to bring the material into space.
Given the size of the Death Star, the surface area would be 24052.8 square miles, or 7.45x10^10 square yards. One company I found in Los Angeles produces 1.5 million yards of fabric per week! The outer structure of the space station would be maintained simply by air pressure, but a lightweight steel skeleton could be used to give the station more definition, and provide anchor points for interior walls and equipment.
It would take 955 years for one company at the above output to make the fabric necessary. However, there are 18,783 textile mills in the USA alone. If all worked at the above output we could have the skin of the Death Star done in a few weeks. Keep working for six months and we'd have more than we needed! The U.S. produces $12.5 billion worth of textiles per year, a number that we could by 10 to still have a safe estimate that considers the higher quality materials we'd need to manufacture.
If we decide not to create artificial gravity, we can also do away with most structural considerations. Our heavy equipment just needs to be secured in several directions, but without the force of gravity pulling it downwards it becomes a trivial matter.
The trickiest part is the weapons system and power generation, but private industry is well on the way to solving both of those problems. Add in the necessary force field and shields, and we could be well on our way to being the proud owners of our own Death Star. Might as well throw some cloaking in too, while we're at it!
Assuming that the technology for generating necessary power and weapons is already available when construction commences, I estimate that a fully operation Death Star could be casting shadows of terror over peaceful planets in only a few decades, and at a very affordable price!