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Is it possible that a region of spacetime rotating with any objects inside it? In this case we don't need a dark matter to explain why distant stars have so big orbital speed. They moving with normal orbital speed inside spacetime, but spacetime also is moving and we see the sum of this speeds.

Is it possible to prove it?

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  • $\begingroup$ Not within general relativity as the theory of gravity. Maybe you have an alternate theory of gravity? $\endgroup$
    – Dan
    Commented Feb 9, 2022 at 14:06
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    $\begingroup$ please see the description of the dark-matter tag for the many observations that require dark matter, other than rotation curves of galaxies $\endgroup$
    – rfl
    Commented Feb 9, 2022 at 19:03
  • $\begingroup$ Additionally, if the extra unseen mass is actually due to spacetime rotating (and not dark matter rotating), then it would mean that rotating spacetime has some intrinsic mass to it, and I do not think it does. $\endgroup$
    – user261609
    Commented Feb 10, 2022 at 13:03

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It is possible for spacetime to be rotating, though we need to be very careful about what we mean by "rotating" in this context. The spacetime around a rotating black hole is rotating in this sense. Mathematically we describe the rotation using an equation called the Kerr metric.

But spacetime cannot just rotate in any arbitrary way. The geometry of spacetime, including its rotation, is linked to the way matter and energy are distributed in that spacetime by Einstein's equation for general relativity. The geometry of the spacetime outside a rotating black hole is controlled by the mass and angular momentum of the black hole.

So the geometry of the spacetime in and around a rotating galaxy is controlled by the mass and angular momentum of the galaxy. We can calculate this and in fact we find the "rotation" of the spacetime in and around the galaxy is so small it can be completely ignored. It certainly could not affect the motion of the stars orbiting in the galaxy.

So the answer to your question is that we cannot explain the orbital motion of stars inside galaxies by rotating spacetime, because any rotation of spacetime is determined by those stars. We do need there to be dark matter present in the galaxy.

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We have two options for this model, and both lead to a bad explanation as I see it.

Is the axis of rotation within the observable universe? Then we would see it, it would be an axis where expansion speed is zero. We dont see it.

Is the axis of rotation outside of the observable universe? Then we would still see a difference in expansion speed in different edges of our observable universe. We dont see it.

You could say that axis of rotation is so far away, that even the difference is undetectable. But then what is the difference with just an expansion? Parts are so far away that they dont affect each other, and we have no benefit of considering it a rotation any more. Locally it will not differ in any way.

Also the change of the expansion speed cant be explained with it either.

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  • $\begingroup$ I asked about Dark Matter in galaxy, not the Dark Energy of Universe $\endgroup$
    – Robotex
    Commented Feb 10, 2022 at 14:26

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