How does gravitational self-interaction affect the Milky Way Galaxy?

[KurtLudwig]

It is believed that gravity interacts with itself. I assume that gravity between stars increases. Does gravitational self-interaction change the galaxy's shape or increase the rotation curves of stars?

 

[PeterDonis]

It is believed that gravity interacts with itself.

More precisely, the Einstein Field Equation is nonlinear, which can be described as gravity interacting with itself. There is a lot of complexity lurking here; see this Insights article series for more information:

https://www.physicsforums.com/insights/does-gravity-gravitate/

I assume that gravity between stars increases.

No, gravity interacting with itself is not that simple.

Does gravitational self-interaction change the galaxy's shape or increase the rotation curves of stars?

The standard viewpoint at present is that any such effect is negligible, because gravity is too weak in this regime for any nonlinear effects to be significant. This is one of the chief reasons why the standard viewpoint postulates dark matter in order to account for galaxy rotation curves.

There is a body of research by Deur, among others, that claims that the above is not the case. This research has been discussed in a number of PF threads. I think it's fair to say that these proposals have not achieved much traction in the wider community, although research along these lines continues.

There is also the MOND viewpoint, which claims, in effect, that GR does not correctly describe the law of gravity for very small "acceleration due to gravity". (Many MOND proponents do not describe their research this way, but that is what it amounts to.)

 

[KurtLudwig]

Thank you so much for taking the tine to answer my questions.
I attempted to understand your insights article "does-gravity-gravitate", however I am not at your level. One actually has to study physics at a graduate level and take classes in General Relativity to understand.
Is professor Alexander Deur mathematics correct? As you know, he is a reasearch physicist in particle physics at Jefferson Labs in Virginia.

 

[PeterDonis]

Is professor Alexander Deur mathematics correct?

That is an open question. If you search PF for his name you will find multiple threads discussing his work. I am not aware of any other physicist who has confirmed his calculations.