Rotation of a massive disc?

[steveupson]

Frame dragging is a very specific example of rotating spacetime. Are there any other examples that have been theorized or proven? The specific example that comes to mind is the effect of a rotating massive disk on local spacetime. For example, the rings of Saturn might cause a local rotation in the spacetime surrounding the planet and that this rotation interacts with adjacent non-rotating space in order to create unexplained high winds along the equator of the planet's surface.

 

I often have difficulty when researching things like this because it isn’t much talked about, and if it has been explored then it usually goes under some obscure name that makes it even more difficult to find. Do you know if rotating massive discs have been looked at mathematically?

 

The difference would seem to be, at first glance, that frame dragging occurs in the field outside of the rotating mass while this other type of rotating spacetime would occur in the field that is inside the rotating mass.

Edited June 3, 2017 by steveupson

[Mordred]

Yes the rotating disks have been mathematically looked at. The leading theory is called Density waves. In many ways its similar to how Galaxies form spiral arms.

 

Here is a generalization of the involved mathematics which follow in its basis the virial theorem and other hydrodynamic equations such as Jeans instability.

 

https://www.google.ca/url?sa=t&source=web&rct=j&url=http://astro.pas.rochester.edu/~aquillen/ast570/lectures/E_SpiralDensity.pdf&ved=0ahUKEwiL4NuZo6LUAhULwWMKHQtnDswQFgg8MAQ&usg=AFQjCNF4uvWsaaexD6ZMESkg_izhNLKzFA&sig2=KeM5nWQCXOLwFVpsELDxrQ

 

The topic is extremely extensive with a huge body of research. Enough that one could make a career of study.

[Janus]

Frame dragging is a very weak effect. It took very sensitive equipment just measure it for the rotating Earth, which is has something in the order of 200,000 times the mass of Saturn's ring system.

[Mordred]

Here is density waves involvement in Saturn's rings.

https://www.google.ca/url?sa=t&source=web&rct=j&url=https://arxiv.org/pdf/1304.3735&ved=0ahUKEwjXmfXvpqLUAhVG1WMKHWD0BysQFggdMAA&usg=AFQjCNFsUAA9UskxhChBjInyl4WXUdsn2Q&sig2=cyLtxrRa-p9-vmS8I5fD7w

 

As Janus pointed out its not exclusively due to frame dragging, any rotating point of attraction can produce density waves including the electromagnetic force.

[Manticore]

You might find this interesting.

 

'Rotating Cylinders and the Possibility of Global Causality Violation.'

Frank J.Tipler

 

Available as PDF from: http://theophysics.host56.com/pdf/tipler-rotating-cylinders.pdf