This is complex subject and I was reading that most of the science can be done by Newtonian but only precision effect calculation requires general relativity. Then there is dark matter also which contributes to gravitation. And the amount of dark matter in local area is also very small. Therefore, is it right to think that a suitable distribution of this dark matter along with the central mass can give same precision effect. GR = Newtonian on (central mass + dark matter). By considering some (may be weird) dark matter distribution around a mass, can the above lead to GR type accuracy.

While there have been attempts to adjust/modify Newtonian gravity in order to match the large scale predictions of GR, it's clear pure Newtonian gravity plus dark matter cannot equal GR. This was proven by the Gravity Probe B ( https://en.wikipedia.org/wiki/Gravity_Probe_B ) experiment, which demonstrated that there are indeed measurable effects that GR predicts, that Newtonian gravity cannot; not even when dark matter is taken into account.

I am not familiar with the details either... Perhaps this will help: https://www.nasa.gov/mission_pages/gpb/ check out the "Gravity Probe B in a Nutshell" and "Gravity Probe B Overview Presentation" links.

I checked but could not figure out how the simple Newtonian on object + suitable dark matter distribution is ruled out. Yes consider non spinning object for time being, probably this experiment was for spin aspect.

It's not about the spin, it's about the frame dragging. GR predicts that heavy objects drag the local spacetime with them. This effect doesn't exist with Newtonian gravity at all, not even when you add dark matter. Gravity Probe B measured this effect, and it was as GR predicted, and in conflict with Newtonian gravity. There is no "suitable" dark matter distribution that can reproduce this effect.

Oops, some conceptual issues in above. I don't think it's like a heavy non spinning yet moving object dragging the spacetime with it. It's about rotation. Frame dragging talks about rotating central mass with angular momentum. https://en.m.wikipedia.org/wiki/Frame-dragging

The lead of that article already says "for instance" when it mentions rotations. If you scroll further down, it explicitly mentions (in bold even) linear frame dragging. So no, there need not be a rotating mass involved.

yes, yes, it talks about the possibility of the same. But admittedly not much work on this. Therefore we consider only a static non spinning object and a suitable dark matter distribution. Can it model gravity?

It's an untested prediction right now, true, but considering the success of all the other predictions made by GR, I'd say it's more likely than not to be true as well. Can what model gravity? Sorry, I don't understand your question?

That is GR = Newtonian on (central mass + some dark matter distribution) Can we divide GR in two components one is simply central mass effect as per Newtonian and second is dark matter profile effect? For static non spinning object case only to start with.

The mere fact of gravitational redshift can only be consistently explained as implying gravitational time dilation. Which in turn inevitably implied non-linearity of gravity. Newtonian strictly \(\frac{1}{r^2}\) in vacuo gravity has no room for redshift. Adding Newtonian gravity conforming dark matter cannot logically change that. Recall that Appendix A "Einstein's Elevator...." derivation I linked to in another thread? [Interestingly, only a short while earlier, I posted a torpedo style response in another forum, to someone's pet idea of -ve mass neutrinos 'explaining' dark matter.]

That is not possible in general, no. All kinds of relativistic effects cannot be modeled that way. For example: the speed of light being finite. Or, when doing detailed calculations, other irresolvable problems are encountered, such as the precession of Mercury. In fact, many (if not all) of the tests mentioned on the following Wikipedia article would be problematic for Newtonian gravity, with or without dark matter: https://en.wikipedia.org/wiki/Tests_of_general_relativity Dark matter merely adds mass. So in the solar system (assuming spherical symmetry for the mass distributions, save for the planets themselves) it would only add a radial component. That component could be simplified through the shell theorem to either adding it to the solar mass, or it would cancel it out. In other words, by adding dark matter to the equation, the only tunable parameter you get is an increase to the sun's mass. That cannot explain all the relativistic effects we see in the solar system. (I don't know if there could be a specific non-spherically-symmetric configuration of dark matter that could explain this, but I highly doubt such an extremely contrived configuration would be stable.) So no, GR cannot be replaced by "Newtonian on (central mass + some dark matter distribution)", not even in our solar system alone.

There are a few of them 1. Mercury precession 2. Gravitational Lensing 3. Gravitational Redshift you think that #3 cannot be explained by Newtonian but what about #1and #2 if the suitable dark matter distribution profile is added around central mass. Below portion is added afterwards in edit mode. Pl see the first para of the link below http://www.einstein-online.info/spotlights/redshift_white_dwarfs.html This appears to me in contrast with your claim.

1. Mercury precession: Can't work because the sign of the known 'anomalous' perihelion advance would be wrong. In any viable metric theory, positive advance can be attributed to departure from Newtonian \(\frac{1}{r^2}\) gravity such that the decline with r is greater than \(\frac{1}{r^2}\). A dark matter 'atmosphere' would have gravity declining at less than the in vacuo Newtonian rate, hence wrongly predicting perihelion retreat. 2. Gravitational Lensing: Would differ from GR and the like, by a factor of 2 - being less in the Newtonian gravity case. Other factors afaik rule out a possible Newtonian gravity lensing by DM. 3. Gravitational Redshift: I suggest reading through this article: https://arxiv.org/abs/physics/9907017v2 The author fails to mention any such Newtonian correspondence in weak field situation lacks logical consistency. If it were just a case of light 'tiring' in escaping a gravitational potential, it would very quickly lead to a 'pile-up crisis'. Consistency requires the true explanation to be one of differential clock-rates between two gravitational potential levels, which isn't allowed in Newtonian gravity. A metric theory where clocks (and rulers) are effected by gravity is inevitable. Again - read that article I linked to above.

That link, although appeared reputed, was bad which stated that gravitational red shift does not require GR.