I think I need to ask this question now, because it's in my mind for several years and I just can't find an answer to it.
After observations of those galaxtic rotation curves, it's pretty clear, that there must be some additional thing, responsible for the additional gravity that is needed to hold those galaxies together.

Dark matter is what would be a easy explaination -> just more matter, not visible to us.

But wouldn't the most simple explaination just be, that the spacetime around the galaxy is warped? Doesn't it make sense for such big things to have a "torsional force" to spacetime itself?
Maybe our frame of reference is warped as well, so if a star in a far away galaxy goes around in a circle, it's just our observation from our point of view.
Here is a quick sketch of what I mean: It's not perfect, but with the explaination I think it makes a lot of sense. If our frame of reference or the spacetime is torn like this, we could actually observe stars moving in a circle while in reality they are not moving in a circle around the galaxy but in a more straight line away from it, if that makes sense. So it depends on the frame of reference ;)



I am not sure if it's the same thing described here, because I am not a physicist :(
https://en.wikipedia.org/wiki/Frame-dragging



But to me this makes the most sense and is the most easy explaination for this problem.
You should never trust your eyes only if relativity is involved so I want to know if a real scientist had the same idea once and did some calculations ^^
This question has been in my head for years and finally it's out now, please don't roast me >_<

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I never cared for this reasoning that the outer stars are orbiting too fast and that there must be more mass outside of the visible areas of galaxies. ESA Gaia mission shows the orbits of stars are not circular or constant speeds around the galactic center. Some have orbits like comets which would seem to throw off the idea that the stars are rotating with similar periods and thus too fast in the outer regions.
https://www.youtube.com/watch?v=z6xdKs9KlCQ

Hello,

Thanks for the very good question! Luckily, others have also considered this effect as a possible explanation for dark matter. In fact, it's a popular debate topic on physics/astronomy forums:

https://www.physicsforums.com/threads/can-rotational-frame-dragging-instead-of-dark-matter-explain-the-rotation-speed-of-galaxies.992260/
https://astronomy.com/news/2018/05/the-case-against-dark-matter
https://forum.cosmoquest.org/showthread.php?137999-Dark-matter-vs-frame-dragging-has-anyone-done-the-math

It certainly is tempting to come up with some alternative theory for dark matter in the absence of any definitive proof of a dark matter particle. These theories are definitely attractive for the same reason that MOND (MOdified Newtonian Dynamics) and other non-dark matter cosmological theories are. The problem is that the frame-dragging effect that you describe comes from a mathematical structure called the Kerr Metric, which describes the shape of spacetime near a rotating black hole. Since the Kerr Metric is a very bad match for the Milky Way's gravitational shape, it's not a very good idea to extrapolate results from the Kerr Metric to things like galaxies, which are distributed over much more space than a black hole. As you can see from the links above, the Lense-Thirring effect in the outer portions of the Galaxy are many, many times smaller than the effects of Newtonian gravity. No one has been able to show that frame dragging would produce a substantial contribution to the rotation curve, much less one that could actually explain the observed rotation curve.

It may seem foolish that scientists put so much faith in the dark matter hypothesis, but the fact of the matter is that there are an extraordinary number of observational, computational, and theoretical tests of dark matter that are able to explain what we see in the Universe. Until another theory comes around that is able to explain all of these observations with the same (or greater!) accuracy as dark matter, the dominant hypothesis will continue to be dark matter.

Hopefully this helps answer your question somewhat.

As for the discussion about the orbits of disk stars near the Sun, I watched the linked video (and enjoyed it a lot!), but I didn't see any "comet-like" orbits or anything else that would cause me to doubt the dark matter explanation. Stars in the local Solar neighborhood are going to have a range of energies/angular momenta, and their orbits aren't all exactly circular. This is a well-known and understood mechanism. Unfortunately I don't know of any non-textbook reading for this phenomenon, but I'm happy to link you to the physics texts about the idea if you would like.

Best,
Tom