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Michael S. Morris and Kip S. Thorne, Wormholes in spacetime and their use for interstellar travel: A tool for teaching general relativity, American Journal of Physics 56, 395 (1988);
https://aapt.scitation.org/doi/abs/10.1119/1.15620
Eric W. Davis, Interstellar travel by means of Wormhole Induction Propulsion (WHIP), AIP Conference Proceedings 420, 1502 (1998);
https://aip.scitation.org/doi/abs/10.1063/1.54779
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A "wormhole" is a good example of the absurdities that result when you initially assume that space is curved, whether in 3-, or 4-dimensions.
When someone talks about curved spacetime, they always reference the "fabric of spacetime" analogy, a 2-dimensional surface, dimpled into the 3rd dimension, presumably due to the presence of a large mass like a planet or star. Certainly, you can add extra dimensions mathematically - like adding more items in a list. As such, General Relativity uses what I would call a curved "model space". But there is no intuitive way to map this model to 3 dimensions of "real space". Consequently, I don't think the model is valid. Useful yes, provides accurate predictions, but it is not a true representation. We are deluded into thinking that accurate predictions made so far can be extended into any regime, that space and be stretched and warped any which way, enabling such things as wormholes, dark energy, inflation, and Hawking Radiation. I don't believe this is true. I don't believe space is curved at all.