Spacetime engineering
One of the great forgotten book of general relativity is Synge's "Relativity : The general theory", which opens with the following line
Of all physicists, the general relativist has the least social commitment. He is the great specialist in gravitational theory, and gravitation is socially significant, but he is not consulted in the building of a tower, a bridge, a ship or an aeroplane, and even the astronauts can do without him until they start wondering which ether their signals travel in.
It has so far been the case that, while its effects are measurable, given sufficient precision, general relativity cannot be used for anything particularly practical outside of its classical limit. While quantum field theory can at least have such esoteric use as nuclear reactor detection via neutrino emission, the practical uses of general relativity remain limited.
This has not stopped people from attempting to do it, either theoretically or in practice, as the theory has much to offer at least in principle with its effects, although none of them even close to being feasible, even in laboratory settings. Because of this, it's a domain precariously perched in between speculative ideas and outright quackery. Proceed at your own risks.
Wormholes
The history of wormholes is, depending on what you're willing to consider, quite long, from Flamm's vague sketch of what would one day become the maximally extended Schwarzschild wormhole in 1916, to Reichenbach's discussion of possible topologies of space in 1928, or the famous paper by Einstein and Rosen.
As an engineering idea, though, outside of various science fiction using the idea of the Schwarzschild wormhole directly without too much consideration for the horizon, the common origin of most wormholes is the Morris-Thorne wormhole. Asked by Carl Sagan for a reasonable method of interstellar travel for his novel Contact, Morris and Thorne devised for the first time a spacetime with the express intent of being used for such a purpose, in their 1987 paper, "Wormholes in spacetime and their use for interstellar travel : A tool for teaching general relativity".
Warp drive
A rigorous idea for the warp drive was first formulated only fairly recently, in Alcubierre's 1994 paper, "The warp drive: hyper-fast travel within general relativity".
Anti-gravity
Anti-gravity within the context of general relativity is, at least on a mathematical level, fairly trivial. Depending on your goals for antigravity, either make the metric around an object flat or make your spacetime such that geodesics diverge rather than converge. Unfortunately, from fairly general arguments, we can see that in all likelihood, this is going to mean violating some energy conditions.
Posted on 2019-12-18 11:14:28