stefan r said:
The observed deviation is the opposite. Particles in the outer galaxy are moving too fast.
Moving too fast yes, as seen from an outside observer. Opposite to what I was saying no.
If the spacetime associated with a galaxy is itself orbiting the galaxy, to an outside observer a particle (or massive object) would appear to have an orbital velocity that is the product of the "orbital" velocity of the involved spacetime and the orbital velocity that would be predicted based on either Newtonian dynamics or general relativity.., because from inside a galaxy, any orbital velocity of the spacetime within the galaxy, would be observable only within the context of its frame dragging affect... and even then almost certainly were dealing with two body interacts.
The point or question is/was, if the spacetime within a galaxy does orbit the galaxy, from within the galaxy it would be dynamically flat and unobservable. It would not add to the basic gravitational interaction of objects inside the galaxy (except as it involves frame dragging). Nor would it create any centrifugal like effect. An object moving moving with the dynamic motion of spacetime, would be essentially at rest realize to the dynamics of that spacetime. That is from within the fish bowl so to speak. Staying within the fish bowl analogy, spacetime would be the water in the bowl and a star in the galaxy a fish. The fish cannot know there is any current in the water without a frame of reference outside the flow of the current... a swimmer caught in a riptide does not know or feel that they are being swept out to sea and they don't experience it more difficult to swim in any direction, a scent an outside frame of reference.
Might a portion of the too fast orbital velocity distant from a galactic center be in part due to the current (the orbit of spacetime) and in part due to the actual orbital velocity of the object?
mfb said:
Frame-dragging scales with (gravitational constant)*(angular momentum)/(2*(radius)3*(speed of light)2). For a satellite in low Earth orbit, you get 10-14/s - this leads to a frame-dragging effect of about 1/100,000 of a degree per year, measurable only with extremely sensitive satellites. For our galaxy, you get 10-25/s, 11 orders of magnitude weaker.
I don't believe your above comment can be applied to the question. It is a two body solution to a massively multi body problem. If you were addressing the interaction between two galaxies it would be a close approximation, as close as we can get at present. But the mass in a galaxy is spread out and for most individual stars or solar systems within the galaxy the curvature of spacetime is affected by a distribution of mass both inside and outside its galactic orbit. It also seems to address only that aspect of frame dragging associated with the axial rotation of a gravitationally significant object, again not well suited to attempting to understand the frame dragging affects of multi body systems. Additionally, my original question relied more on how the predicted linear form of frame dragging might affect the dynamics of spacetime and whether there might be some persistent or even cumulative dynamic affect on spa time associated with the linear frame dragging, of all of the objects in a galaxy over time. (Time here being billions of years.)
And again I am unsure anyone has an answer to the question at present. We have only just begun to dip our toes into the weak field implications of frame dragging associated with gravitationally significant rotating objects. Even there our current experimental data is based on the Earth and the sun both of which have significant gravitational and magnetic fields. Do we need to repeat experiments where the the planet or moon our test satellite orbits has no magnetic field?