# Spacetime distortion and wormholes

Consider the fact that the curvature of spacetime and its relation to matter is given by the EFEs $$R_{\mu\nu}-\frac{1}{2}Rg_{\mu\nu}=\frac{8\pi G}{c^4} T_{\mu\nu}.$$ It is well known that the left side of the EFEs describes the curvature of the spacetime manifold and the right hand side describes the source of the curvature of the spacetime. With this established, lets introduce the Riemann curvature tensor and the metric $$R^\lambda{}_{\mu\nu\sigma}$$ and $$g_{\mu\nu}$$. Furthermore, consider the metric for a wormhole in spacetime given by $$ds^2=g_{\mu\nu}dx^{\mu}dx^{\nu}=-e^{2\phi}dt^2+\left(1-\frac{b}{r}\right)^{\!-1}\!dr^2+r^2(d\theta ^2+\sin^2\!\theta\,d \phi^2).$$ The traversable wormhole metric describes the spacetime geometry such that some object could pass through the distorted spacetime. With this knowledge of the metric and the various tensors needing to describe such a structure embedded in spacetime, consider a new idea similar to the idea of a wormhole but not quite a wormhole (idea is not proven, theoretical, no proper research has been done, just a "for instance"). Consider two points A and B in spacetime separated by $$n$$ light years distance. Now consider some craft that exists near point A and wants to go to point B. This craft can produce immense spacetime curvature (any spacetime curvature desirable). This craft has a desire to get from point A to point B. How would one determine the amount of spacetime curvature needed to reduce the travel time of the craft located at point A, such that the spacetime curvature generated brings point A and B closer together in spacetime? The curvature would also have to be between the two points.

• Are you thinking of this hypothetical technology?
– Sal
Nov 25, 2021 at 21:20
• @Sal Not the warp drive. Im thinking of a craft that can distort spacetime between two points such that it reduces the distance from light years to miles not using warp technology but an intense gravitational field.
– aygx
Nov 26, 2021 at 0:59
• @aygx what is the difference between "intense gravitational field" and "warp" in this context?
– Kosm
Nov 26, 2021 at 8:12
• None, what I mean by warp is bend the space between the points A and B so much that it reduces the distance between them. Like a wormhole but it's not, it's like a one way wormhole. Almost like bringing the destination to the source, so like bringing point B to point A via distortion of spacetime.
– aygx
Nov 26, 2021 at 20:44
• it is not that complicated to come up with field geometries that result in spacetime shortcuts (relative to the Minkowski background), but all of them (that I'm aware of) require physically unrealistic sources. Traversable wormholes require matter that violate energy conditions that for the most part, are known to hold within known matter and fields. Other arrangements that don't rely on matter that violate such energy conditions may still be unrealistic (say, due to inducing deformations that can only exist within the ergosphere of a spinning black hole) Dec 4, 2021 at 2:52