I’m trying to figure out if gravitational fields and gravity interactions can produces the same results as space curves to cause gravitational attraction. I keep getting stuck at the gravity field potential at radius x from the source is somehow related to the curve distance x and curve angle or something. Any chance fields can produce the same results as curves?

Without going into the maths of the subject you touched, I do have an unconvential explantion where curvature is gravity. It's been written down in an article called 'Metric Science'. For a direction of an answer to your question I would have a good look at the chapter 'Gravitation in relation to curvature', it might somehow give you an answer. Though very unconventional physics. More on http://www.sciforums.com/threads/theory-of-everything.162280/

They can produce pretty much the same results in most low mass conditions, but the Newtonian "force" gravity breaks down fairly quickly as mass rises, after which it start producing false results. I assume you have studied the Eddington Experiment? It pretty much clinched Einstein's curved spacetime theory.

No, never even heard of it. Checking it out thanks. I was just thinking curves and fields and didn't consider the Newton, Einstein relation. Please Register or Log in to view the hidden image!

You'll have to define "gravitational fields", "gravity interactions" and "space curves" for me, since I'm not quite sure what you're asking. The Newtonian picture of gravity uses gravitational fields to describe gravitational attraction, and it works fine in a lot of circumstances. The general relativistic picture of gravity uses curved spacetime to describe gravitational attraction, and it works even better. Maybe it would help if you posted the relevant mathematics. Show us where, exactly, you're getting stuck. Newtonian gravity and relativity produce similar results in a lot of cases. Is that what you're asking? What kind of results are you looking for? What are you trying to describe or calculate?

One other thing is speed. Although not attraction, Gravitational waves in GR travel at the speed of light. With Newton, the influence of the change of positon of mass would be instantaneous over the field. https://www.ligo.org/science/GW-GW.php

Umm, didn't they detect gravitation waves a few years ago? Is the gravitational wave, a wave in the gravitational field? In relativity is there spacetime curves and gravitational fields/waves? And is that why its different to Newtons field only theory? Like a magnetic field, but its a gravity field. Can Newtons field theory be modified to produce the same results as relativity? Why when mass is added does Newtons field theory produce incorrect results? It must be missing something? DM, DE, curves or ? Yes sort of, I was confused because sometimes I read people talking about curves and sometime fields so I was trying to compare them. I didn't think Newton fields and Einstein curves and both are valid under certain conditions, Dave's post linked the correlation for me.

BdS: Roughly speaking, Newtonian gravity is a sort of approximation to general relativity, which works well enough as long as the gravity is not too strong. It is not really possible to modify Newtonian gravity to make it more like GR, because the two descriptions of what gravity is are fundamentally different. Newtonian gravity describes gravity as a force that acts on mass. GR describes gravity as an effect of curved spacetime, that curvature being due to mass (and some other things). Gravitational waves are really a prediction of GR, not so much Newtonian gravitation.